
<PAGE>   1

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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                            ------------------------
 
                                 SCHEDULE 14D-1
              TENDER OFFER STATEMENT PURSUANT TO SECTION 14(d)(1)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                            ------------------------
 
                         AMERICAN MEDSERVE CORPORATION
                           (NAME OF SUBJECT COMPANY)
 
                           OMNICARE ACQUISITION CORP.
                          A WHOLLY OWNED SUBSIDIARY OF
 
                                 OMNICARE, INC.
                                   (BIDDERS)
 
                    COMMON STOCK, PAR VALUE $0.01 PER SHARE
                         (TITLE OF CLASS OF SECURITIES)
 
                                   027448109
 
                     (CUSIP NUMBER OF CLASS OF SECURITIES)
                            ------------------------
                                JOEL F. GEMUNDER
                                   PRESIDENT
                                 OMNICARE, INC.
                         50 EAST RIVERCENTER BOULEVARD
                           COVINGTON, KENTUCKY 41011
                                 (606) 291-6800
          (NAMES, ADDRESSES AND TELEPHONE NUMBER OF PERSON AUTHORIZED
          TO RECEIVE NOTICES AND COMMUNICATIONS ON BEHALF OF BIDDERS)
 
                            ------------------------
 
                                WITH COPIES TO:
                                MORTON A. PIERCE
                                DEWEY BALLANTINE
                          1301 AVENUE OF THE AMERICAS
                            NEW YORK, NEW YORK 10019
                                 (212) 259-8000
                           CALCULATION OF FILING FEE
 
<TABLE>
<CAPTION>
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                TRANSACTION VALUATION*                                 AMOUNT OF FILING FEE
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<S>                                                   <C>
                     $229,230,950                                            $45,846
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</TABLE>
 
* Estimated for purposes of calculating fee only. The calculation assumes the
  purchase of (i) 12,217,936 shares of Common Stock par value $0.01 per share
  (the "Shares"), issued and outstanding as of August 7, 1997, and (ii) 517,117,
  Shares issuable upon the exercise of presently outstanding stock options, in
  each case, at a price per Share of $18.00 in cash.
 
[ ] Check box if any part of the fee is offset by Rule O-11(a)(2) and identify
    the filing with which the offsetting fee was previously paid. Identify the
    previous filing by registration statement number, or the Form or Schedule
    and the date of its filing.
 
<TABLE>
                <S>                                    <C>
                Amount Previously Paid:                NOT APPLICABLE
                Form or Registration No.:              NOT APPLICABLE
                Filing Party:                          NOT APPLICABLE
                Date Filed:                            NOT APPLICABLE
</TABLE>
 
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<PAGE>   2
 
   CUSIP No.  027448109
 
<TABLE>
<S>        <C>                                                                                       <C>
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  1        NAME OF REPORTING PERSON: OMNICARE ACQUISITION CORP. S.S. OR I.R.S. IDENTIFICATION NO. OF
           ABOVE PERSON: 31-1554409
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  2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (a) [ ] (b) [ ]
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  3        SEC USE ONLY
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  4        SOURCES OF FUNDS AF
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  5        CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(e) OR 2(f) [    ]
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  6        CITIZENSHIP OR PLACE OF ORGANIZATION STATE OF DELAWARE
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  7        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON NONE
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  8        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (7) EXCLUDES CERTAIN SHARES [ ]
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  9        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (7) N/A
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  10       TYPE OF REPORTING PERSON CO
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</TABLE>
 
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<PAGE>   3
 
   CUSIP No.  027448109
 
<TABLE>
<S>        <C>                                                                                       <C>
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  1        NAME OF REPORTING PERSON: OMNICARE, INC.
           S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON:  31-1001351
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  2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (a) [ ] (b) [ ]
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  3        SEC USE ONLY
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  4        SOURCES OF FUNDS WC/BK
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  5        CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(e) OR 2(f) [    ]
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  6        CITIZENSHIP OR PLACE OF ORGANIZATION STATE OF DELAWARE
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  7        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON NONE
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  8        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (7) EXCLUDES CERTAIN SHARES [ ]
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  9        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (7) N/A
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  10       TYPE OF REPORTING PERSON CO
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</TABLE>
 
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<PAGE>   4
 
     This Statement relates to a tender offer by Omnicare Acquisition Corp., a
Delaware corporation (the "Purchaser") and a wholly owned subsidiary of
Omnicare, Inc., a Delaware corporation ("Parent"), to purchase all outstanding
shares of common stock, par value $0.01 per share (the "Shares"), of American
Medserve Corporation, a Delaware corporation (the "Company"), at a purchase
price of $18.00 per Share, net to the seller in cash, without interest thereon,
upon the terms and subject to the conditions set forth in the Offer to Purchase
dated August 14, 1997 (the "Offer to Purchase") and in the related Letter of
Transmittal (which, as amended or supplemented from time to time, together
constitute the "Offer"). Copies of the Offer to Purchase and the Letter of
Transmittal are annexed to and filed with this Statement as Exhibits (a)(1) and
(a)(2), respectively.
 
ITEM 1. SECURITY AND SUBJECT COMPANY.
 
     (a) The name of the subject company is American Medserve Corporation, a
Delaware corporation. The principal executive offices of the Company are located
at 184 Shuman Boulevard, Naperville, Illinois 60563.
 
     (b) The exact title of the class of equity securities being sought in the
Offer is the common stock, par value $0.01 per share, of the Company. The
information set forth in the Introduction to the Offer to Purchase is
incorporated herein by reference.
 
     (c) The information set forth in Section 6 ("Price Range of Shares;
Dividends on the Shares") of the Offer to Purchase is incorporated herein by
reference.
 
ITEM 2. IDENTITY AND BACKGROUND.
 
     (a) through (d) and (g). This Statement is being filed by the Purchaser and
Parent. The information set forth in the "Introduction," Section 9 ("Certain
Information Concerning the Purchaser and Parent") and Schedule I of the Offer to
Purchase, is incorporated herein by reference.
 
     (e) and (f). None of the Purchaser or Parent, nor, to the best of their
knowledge, any of the persons listed in Schedule I of the Offer to Purchase, has
during the last five years (i) been convicted in a criminal proceeding
(excluding traffic violations or similar misdemeanors) or (ii) been a party to a
civil proceeding of a judicial or administrative body of competent jurisdiction
and as a result of such proceeding was or is subject to a judgment, decree or
final order enjoining future violations of, or prohibiting activities subject
to, federal or state securities laws or finding any violation of such laws.
 
ITEM 3. PAST CONTACTS, TRANSACTIONS OR NEGOTIATIONS WITH THE SUBJECT COMPANY.
 
     (a) and (b). The information set forth in the "Introduction," Section 9
("Certain Information Concerning the Purchaser and Parent"), Section 11
("Background of the Offer") and Section 12 ("Purpose of the Offer and the
Merger; Plans for the Company; Proposed Merger") of the Offer to Purchase is
incorporated herein by reference.
 
ITEM 4. SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.
 
     (a) and (b). The information set forth in Section 10 ("Source and Amount of
Funds") of the Offer to Purchase is incorporated herein by reference.
 
     (c) Not applicable.
 
ITEM 5. PURPOSE OF THE TENDER OFFER AND PLANS OR PROPOSALS OF BIDDER.
 
     (a) through (e). The information set forth in the "Introduction," Section
11 ("Background of the Offer") and Section 12 ("Purpose of the Offer and the
Merger; Plans for the Company; Proposed Merger") of the Offer to Purchase is
incorporated herein by reference.
 
     (f) and (g). The information set forth in Section 7 ("Effect of the Offer
on the Market for the Shares; Nasdaq Stock Market Listing; Exchange Act
Registration; Margin Regulations") of the Offer to Purchase is incorporated
herein by reference.
 
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<PAGE>   5
 
ITEM 6. INTEREST IN SECURITIES OF THE SUBJECT COMPANY.
 
     (a) and (b). The information set forth in the "Introduction," Section 9
("Certain Information Concerning the Purchaser and Parent") and Schedule I of
the Offer to Purchase is incorporated herein by reference.
 
ITEM 7. CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT TO
        THE SUBJECT COMPANY'S SECURITIES.
 
     The information set forth in the "Introduction," Section 9 ("Certain
Information Concerning the Purchaser and Parent"), Section 11 ("Background of
the Offer"), Section 12 ("Purpose of the Offer and the Merger, Plans for the
Company; Proposed Merger") and Schedule I of the Offer to Purchase is
incorporated herein by reference.
 
ITEM 8. PERSONS RETAINED, EMPLOYED OR TO BE COMPENSATED.
 
     The information set forth in the "Introduction" and Section 16 ("Fees and
Expenses") of the Offer to Purchase is incorporated herein by reference.
 
ITEM 9. FINANCIAL STATEMENTS OF CERTAIN BIDDERS.
 
     The information set forth in Section 9 ("Certain Information Concerning the
Purchaser and Parent") of the Offer to Purchase is incorporated herein by
reference.
 
     The incorporation by reference herein of the above-mentioned financial
information does not constitute an admission that such information is material
to a decision by a security holder of the Company whether to sell, tender or
hold securities being sought in the Offer.
 
ITEM 10. ADDITIONAL INFORMATION.
 
     (a) None.
 
     (b) and (c). The information set forth in Section 15 ("Certain Legal
Matters; Regulatory Approvals") of the Offer to Purchase is incorporated herein
by reference.
 
     (d) The information set forth in Section 7 ("Effect of the Offer on the
Market for the Shares; Nasdaq Stock Market Listing; Exchange Act Registration;
Margin Regulations") and Section 15 ("Certain Legal Matters; Regulatory
Approvals") of the Offer to Purchase is incorporated herein by reference.
 
     (e) None.
 
     (f) The information set forth in the Offer to Purchase and the Letter of
Transmittal is incorporated herein by reference in its entirety.
 
ITEM 11. MATERIAL TO BE FILED AS EXHIBITS.
 
      (a)(1) Offer to Purchase, dated August 14, 1997.
 
      (a)(2) Form of Letter of Transmittal.
 
      (a)(3) Form of Letter from Credit Suisse First Boston Corporation, as
             Dealer Manager, to Brokers, Dealers, Commercial Banks, Trust
             Companies and Other Nominees.
 
      (a)(4) Form of Letter from Brokers, Dealers, Commercial Banks, Trust
             Companies and Other Nominees to Clients.
 
      (a)(5) Notice of Guaranteed Delivery.
 
      (a)(6) Guidelines for Certification of Taxpayer Identification Number on
             Substitute Form W-9.
 
      (a)(7) Form of summary advertisement, dated August 14, 1997.
 
      (a)(8) Form of press release issued by Parent on August 8, 1997.
 
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      (b)    None.
 
      (c)(1) Agreement and Plan of Merger, dated as of August 7, 1997, among
             Parent, the Purchaser and the Company.
 
      (d)    None.
 
      (e)    Not Applicable.
 
      (f)    None.
 
                                        6
<PAGE>   7
 
                                   SIGNATURE
 
     After due inquiry and to the best of its knowledge and belief, each of the
undersigned certifies that the information set forth in this statement is true,
complete and correct.
 
Dated: August 14, 1997
                                          OMNICARE ACQUISITION CORP.
 
                                          By:       /s/ Joel F. Gemunder
                                            ------------------------------------
                                                      Joel F. Gemunder
                                                         President
 
                                          OMNICARE, INC.
 
                                          By:       /s/ Joel F. Gemunder
                                            ------------------------------------
                                                      Joel F. Gemunder
                                                         President
 
                                        7
<PAGE>   8
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
EXHIBIT                                    DESCRIPTION                                     PAGE
--------  -----------------------------------------------------------------------------    ----
<S>       <C>                                                                              <C>
 (a)(1)   Offer to Purchase, dated August 14, 1997.....................................
 (a)(2)   Form of Letter of Transmittal................................................
 (a)(3)   Form of Letter from Credit Suisse First Boston Corporation, as Dealer
          Manager, to Brokers, Dealers, Commercial Banks, Trust Companies and Other
          Nominees.....................................................................
 (a)(4)   Form of Letter from Brokers, Dealers, Commercial Banks, Trust Companies and
          Other Nominees to Clients....................................................
 (a)(5)   Notice of Guaranteed Delivery................................................
 (a)(6)   Guidelines for Certification of Taxpayer Identification Number on Substitute
          Form W-9.....................................................................
 (a)(7)   Form of summary advertisement, dated August 14, 1997.........................
 (a)(8)   Form of press release issued by Parent on August 8, 1997.....................
 (b)      None.........................................................................
 (c)(1)   Agreement and Plan of Merger, dated as of August 7, 1997, among Parent, the
          Purchaser and the Company....................................................
 (d)      None.........................................................................
 (e)      Not Applicable...............................................................
 (f)      None.........................................................................
</TABLE>
 
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