Google and prospective partners have held preliminary discussions but have not come up with a formal proposal, and Google may end up deciding not to pursue a bid, the source said.
It is not clear which private equity firms Google has spoken to, the WSJ said.
Representatives of Google could not immediately be reached for comment.
Any potential deal between the two biggest Internet companies would likely arouse antitrust scrutiny.
Google is interested in selling some advertising across Yahoo's websites, the Journal said, citing people familiar with the matter.
Microsoft Corp is now considering financing part of a bid for Yahoo by a private equity firm, people familiar with the matter have said.
Yahoo has been in a state of chaos since it fired former CEO Carol Bartz in early September. The company retained investment banking firm Allen & Co to help conduct a "strategic review" of its business and is reportedly working with executive search firm Heidrick & Struggles to find a new CEO.
A number of potential buyers have expressed interest in a deal with Yahoo. Private equity firms Silver Lake Partners, Providence Equity Partners, Bain Capital, Hellman & Friedman, Blackstone Group, and KKR are among those likely to get a look at the limited financial data Yahoo's advisers are circulating.
(Reporting by Matthew Lewis in Chicago; Editing by Vicki Allen)