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 on Monday.

As part of the deal Yahoo would put its Asian assets, including significant minority stakes in Yahoo Japan and China's Alibaba Group, up for sale, 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 on Monday, before closing up 2 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 international assets at $9.25 billion, according to a research note he published on Monday.

"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.

Shares in both Yahoo Japan and Alibaba.com Ltd dropped 4 percent on the new proposal, thanks to the greater uncertainty now hanging over the two companies.

"We had always looked at Yahoo Inc teaming up with Microsoft as a positive for Yahoo Japan," said Macquarie Securities analyst Nathan Ramler.

"The fact that Yahoo Japan is potentially not included is a concern," he said, adding that the Japanese company could have benefited from Microsoft's expertise in software, personal computers and its deep pockets.