BOSTON (Reuters) - Microsoft Corp. has proposed to buy Yahoo Inc.'s search business and take a minority stake in the web pioneer, stopping short of a full-out merger, a person familiar with the discussions said yesterday.

As part of the deal, Yahoo would sell its Asian assets including significant minority stakes in Yahoo Japan and China's Alibaba Group, while Microsoft would buy a chunk of what remains of the company, the source said.

The talks were revealed by the two companies on Sunday, but they declined to reveal the terms of the discussions. Earlier this month, Microsoft walked away from a proposal to acquire Yahoo for $47.5 billion, or $33 per share, after Yahoo rebuffed the offer, saying it would only settle for $37 a share.

The new deal, if completed, would forge an alliance between the two companies that would represent an alternative means of competing with rival Google Inc, whose ubiquitous search engine has made it an online advertising powerhouse.

The proposal represents an outline of Microsoft's current thinking and it does not yet put a value on Yahoo's search business, said the source, who was not authorized to speak on the record because the discussions are confidential.

Microsoft and Yahoo representatives declined to comment.

Shares of Yahoo fell as much as 0.87 percent yesterday, before closing up two cents at $27.68 on Nasdaq. Microsoft dropped 1.8 percent to $29.46.

Collins Stewart analyst Sandeep Aggarwal estimates Yahoo's search advertising business is worth about $21 billion, while putting the value of its its international assets at $9.25 billion, according to a research note he published yesterday.

"Microsoft is the most interested in Yahoo Search," said Aggarwal, who added that Microsoft may buy parts of Yahoo for a premium or buy all of Yahoo and then spin off certain assets.

Microsoft said on Sunday that it was talking with Yahoo about an alternative transaction that did not involve a full buyout after withdrawing its sweetened $47.5 billion bid for the company on May 3.

Yahoo is a distant second to Google Inc. in web search in the US, and Microsoft is third.

Combined, Yahoo and Microsoft would have around a 30 percent US share, compared with Google's roughly 60 percent, according to figures from research firm comScore. Google's lead is even larger on a global basis, according to comScore.