Since buying out Yahoo! seemed too expensive, Microsoft is back again with another offer. Microsoft's Statement:

In light of developments since the withdrawal of the Microsoft proposal to acquire Yahoo! Inc., Microsoft announced that it is continuing to explore and pursue its alternatives to improve and expand its online services and advertising business. Microsoft is considering and has raised with Yahoo! an alternative that would involve a transaction with Yahoo! but not an acquisition of all of Yahoo! Microsoft is not proposing to make a new bid to acquire all of Yahoo! at this time, but reserves the right to reconsider that alternative depending on future developments and discussions that may take place with Yahoo! or discussions with shareholders of Yahoo! or Microsoft or with other third parties.

There of course can be no assurance that any transaction will result from these discussions.

From AllThingsD:

The software giant would not give details, but sources at both companies said it involved Microsoft buying Yahoo’s search business and the ad business related to text-based ads.

Kevin Johnson also posted an internal Microsoft memo on News.com.