The Wall Street Journal said that News Corp was eyeing a move that would see MySpace and other of Murdoch's web interests merge with Yahoo.
Yahoo would give News Corp 20% of its shares under the alleged deal, allowing it to remain independent.
Microsoft has offered to buy Yahoo for more than $40bn (£20.5bn).
However Yahoo has dismissed the move as undervaluing its brand, audience, investments in advertising platforms and future growth prospects, free cash flow and earnings potential.
Google challenge
In a letter outlining why it had spurned the offer, Yahoo chief executive Jerry Yang said that the firm was in a position to take advantage of "a huge market opportunity".
"Today, Yahoo is a faster-moving, better-organized, more nimble company than it was just a few months ago," Mr Yang said.
"We have redeployed our resources to drive Yahoo's key strategic priorities taking important steps to streamline our organisation and close down or scale back businesses that don't support these critical growth initiatives."
Microsoft wants to merge with Yahoo to increase its online presence and enable it to better compete with industry leader Google.
It has said that Yahoo rejecting its offer, worth $31 a share, 62% above the level at which Yahoo stocks were trading when the offer was made on 1 February, was "unfortunate".
News Corp's media interests include Dow Jones - which publishes the Wall Street Journal - Fox News, The Sun and The Times as well as MySpace and a 39% stake in BSkyB.
