The Seattle Post Intelligencer says the deal is imminent. The Wall Street Journal's Kara Swisher reported last week on her All Things Digital blog that Microsoft executives have been in Silicon Valley negotiating.
Unlike the original offer to buy the entire company, Microsoft now appears to be interested only in a tie up with Yahoo's search and advertising business. Yahoo's new CEO Carol Bartz has famously said she's willing to make such a deal for a "boatload of money".
Shares in Yahoo gained 4% in Friday's trading and began Monday's trading 2% to the positive. Neither company has commented on the rumors of a deal.