Shares in Irish biotechnology company Elan Corp
A source familiar with the situation told Reuters on Sunday an agreement on the sale of part of the business could come as early as this week.
Elan is also in talks with a second suitor, but the status of those discussions was unclear.
Selling a minority stake could be the first move in a multistep transaction to sell Elan outright, the source said.
Elan and Bristol-Myers both declined to comment.
Industry analysts said a tie-up between the two companies would make strategic sense since Elan's focus on neurodegenerative diseases matches Bristol-Myers's interest in this area and the U.S. group is keen to grow via external deals.
Shares in Elan were 5.1 percent higher in London by 3:50 a.m. EDT, while the Dublin stock market was closed for a holiday.
In January, Elan hired Citigroup to conduct a strategic review of its business, which it said at the time could lead to a sale or merger of the company.
Elan has been under pressure from investors critical of Chief Executive Kelly Martin's leadership and the state of the biotech company, which is burning through cash at a rapid rate.
Other companies may have difficulty making a full acquisition for the Irish biotech company because of those drug partnership agreements.
Earlier this month, Danish pharmaceutical group Lundbeck
(Reporting by Ben Hirschler and Jessica Hall in Philadelphia; Editing by Jon Loades-Carter)