The New York Post, citing two undisclosed sources familiar with the situation, says that Time Warner and Microsoft are in "advanced discussions".
Time Warner shares rose 2.4% after the story broke.
If the sale goes ahead Microsoft would combine its stake in AOL with its MSN internet unit. MSN and AOL are major rivlas on the internet front.
The two are also rivals in the browser market as well. AOL owns one-time market leader Netscape, which has long been usurped by Microsoft's Internet Explorer.
Last month, Netscape posted the biggest gain to 2.02% of the browser market, as Microsoft's IE dropped to 86.31% percent from 87.2%. Mozilla Corp's FireFox rose a fifth of a point to 8.27%.
According to the Post, Microsoft would pay "some money" to Time Warner for the AOL stake, leaving the two companies approximately equal partners in the venture.
The paper added the deal could happen in the next couple of months.
Analysts are valuing AOL at anything between $10bn and $20bn.
Time Warner and Microsoft declined to comment.
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