Bristol-Myers shares have run up strongly in the past two weeks on talk of a Sanofi bid, closing at $28.52 on Friday to value Bristol-Myers at more than $56 billion.
They fell back in early New York trading, however, while Sanofi put on the third biggest gains in a weak French benchmark CAC-4O index.
Neither company ever confirmed they were in negotiations, but investors viewed the idea of combining the two businesses to form the world's biggest drugmaker as highly credible.
Sanofi and Bristol-Myers have long been tipped as merger partners, since they work together in marketing the hugely successful bloodthinner Plavix and hypertension drug Avapro.
The U.S. firm's lack of a permanent CEO has also made it a target of bid talk.
The issue is complicated, however, by patent litigation over Plavix. A key court case over Plavix patents opened in the United States last month, with the two allies fighting a challenge from Canadian generic drugmaker Apotex. A verdict is not expected before the third quarter of the year.
That legal action is an obstacle to agreeing a fair price for Bristol-Myers, though some analysts have argued that Sanofi -- given its inside knowledge of the situation -- is in a better position to assess the risk than any other potential acquirer.
That relative advantage for Sanofi over rival predators means takeover talk will probably not go away and analysts at Morgan Stanley said persistent M&A speculation was likely to limit near-term upside for Sanofi stock.
Uncertainty over generic competition to its biggest seller Lovenox, following last week's defeat in another U.S. patent case, may also hold back the shares.
In Europe, Sanofi shares rose as much as 2% to an intraday high of 68.85 euros, the stock's highest level in about two weeks.
The shares were up 0.2% at 68.60 euros by 1510 GMT in a sharply weaker market for French blue chip stocks.
Sanofi's ambitious chairman and veteran dealmaker, Jean-Francois Dehecq, will be under pressure to explain his intentions when he presents financial results for the group on Feb. 13.
Gbola Amusa, an analyst at Bernstein, said the rally in Bristol-Myers's stock price had left Sanofi with little opportunity for value creation in any takeover deal but it was unclear whether Sanofi would now back off.
"The extent of (Sanofi) share price gains will likely depend on how far Sanofi's management goes at the Feb. 13 full-year results in making unqualified statements that the window of opportunity for a deal is closed," he said in a note.
Bristol-Myers, meanwhile, has given little indication that it wants to rush into the arms on Sanofi. Indeed, its recent deal with AstraZeneca on diabetes is seen by many analysts as a sign of its desire to remain independent.