"We have great respect for Yahoo, and together we can offer an increasingly exciting set of solutions for consumers, publishers and advertisers while becoming better positioned to compete in the online services market," Steve Ballmer, Microsoft chief executive, said in a statement.
However a US justice department spokeswoman told AP its antitrust division would be "interested in looking at the competitive effects" of any such transaction.
Yahoo was not immediately available for comment.
The company has been losing market share to Google and warned earlier this week that it faced "headwinds" in 2008, forecasting revenue below Wall Street estimates.
On Thursday, Yahoo disclosed that Terry Semel, non-executive chairman, was leaving the board, ending its formal ties with the former chief executive, who is credited with reviving the company and then losing touch.
Semel, replaced as CEO last June, had faced heavy criticism for failing to move faster to meet both rival Google's challenge in web search and advertising and, more recently, the rise of social networking sites such as MySpace and Facebook.
US stock futures jumped on the Microsoft news, which offset a disappointing earnings report from Google late on Thursday.
Paul Mendelsohn, chief investment strategist at Windham Financial Services, said a deal made sense.
"Yahoo is having a really tough time competing against Google. Whether it's a good price, I can't see anybody else who is going to outbid Microsoft," Mendelsohn said.
Microsoft said it had identified four areas that would generate at least $1bn in annual synergies for the combined entity.
Tim Smalls, head of US stock trading at brokerage firm Execution LLC, was less enthusiastic about the benefits of a tie-up.
"Shocking! To me, the premium seems exorbitant, for what is a dwindling business. I personally don't see how the synergies of Microsoft-Yahoo is going to take on Google," Smalls said.