According to the article by Sunday Times business editor John Waples, who did not name his sources, senior directors at Microsoft and Yahoo! have agreed the "broad terms" of a "complex transaction".
The story also claims Jonathan Miller, ex-chairman and chief executive of AOL, and Ross Levinsohn, a former president of Fox Interactive Media, have been lined up to lead the Yahoo! management team.
The pair would borrow $5bn from Microsoft and raise another $5bn from external investors with which they would buy convertible preference shares and warrants giving them a holding in excess of 30% of Yahoo!.
In addition, the terms include a 10-year operating agreement for Microsoft to manage Yahoo! search business and give Microsoft a two-year call option to buy the search business for $20bn.
However, the Sunday Times story has subsequently been denied on the record by Levinsohn as well as rejected by sources at Microsoft and Yahoo!.
Levinsohn told the Wall Street Journal's AllThingsDigital blog that the story was "total fiction".
Blog author Kara Swisher also claims she has spoken to top sources at Yahoo! and Microsoft and "all scoff at such a deal now taking place or that either side has been in any such discussions of late".
But Swisher also admits "That's not to say there will not be some search deal between Yahoo! and Microsoft, which seems more than likely at some point."
Continuing speculation that Microsoft will make another approach for Yahoo!'s search business intensified two weeks ago when Jerry Yang announced he would step down as chief executive once a successor was appointed.
Microsoft first showed its interest when it made a $44.6bn (£29.6bn) bid for the whole of Yahoo! in February. Since then Yahoo!'s market capitalisation has sunk to $16bn.