ImClone (IMCL) said Monday that the mystery bidder that has flirted with paying $70 a share for the company will make up its mind by Wednesday.

The company will either make a firm offer or withdraw by that deadline. ImClone said it will divulge the mystery suitor's name if it withdraws its proposal, according to an ImClone release.

Last week,

Bristol-Myers Squibb

(BMY) - Get Report

went hostile with its own bid for the company, raising it to $62 a share and going directly to shareholders.

ImClone Chairman

Carl Icahn

dismissed the hostile tender offer as "misleading" and "absurd."

TheStreet.com BioTalk: IMCL, BMY

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Investors, and no doubt Bristol Myers, will now wait to hear from the veiled third party.

ImClone is best known for its Erbitux cancer drug, which Bristol-Myers sells in the U.S. German company Merck KGaA sells the drug in Europe.

ImClone shares closed at $63.38 Friday.