The discussions remain tentative and could collapse after the departure of Terry Semel as Yahoo!'s chief executive and his replacement by Jerry Yang this week.
Yang, co-founder of Yahoo! and incoming chief executive, yesterday pledged to "dig in" to his new role, and acknowledged the difficult task he faces to arrest the decline in the Internet portal's shares.
News Corp, the parent company of FOXNews.com, is interested in a deal even if it means losing some control of MySpace because it would give the media group exposure to a far larger Internet-based business.
Other News Corp digital assets, including the games network IGN, bought in 2005 for $650 million, are also thought to have been offered to Yahoo!.
A deal would demonstrate a remarkably swift return on News Corp's investment in MySpace, which it acquired for $580 million in summer 2005.
Yesterday, Yahoo! was worth $37 billion. A quarter stake in an enlarged company would be worth $12.3 billion.
It is not clear whether Yahoo! was willing to accept the terms offered, even though it has been eager to break into social networking to catch up with Google. Yahoo! tried and failed to buy Facebook, the No. 2 social networking site, for $1 billion last year.
A News Corp source said that Rupert Murdoch, the company's chairman and chief executive, remained committed to the Internet, although he has conceded in an aside in a recent interview with The Wall Street Journal that the privately owned Facebook was gaining ground. Asked whether newspaper readers were drifting off to MySpace, Murdoch joked: "I wish they were. They're all going to Facebook at the moment."
The revelation of discussions with Yahoo! over MySpace comes as News Corp is pursuing a $5 billion bid for Dow Jones. Although Dow is best known for publishing The Wall Street Journal, News Corp believes financial information is a fast-growing digital business.
Meanwhile, Pearson, owner of the Financial Times, is in initial discussions with General Electric, owner of the NBC Universal media group, about a possible counter-bid for Dow. Pearson and GE would, respectively, inject the FT and CNBC into an enlarged Dow, and take 45 per cent each, leaving Dow's Bancroft family with a tenth.
The idea is to commit no capital from Pearson, a deal that could appeal to some shareholders unwilling to see the British company go head-to-head with News Corp with its own cash-based bid.
Yesterday, shareholders privately expressed support for Richard Buxton, of Schroders, who indicated he did not want to see a cash bid, but would be willing to look at a paper-based deal.
Separately, News Corp is hoping to raise $400 million by selling a quarter stake in its outdoor advertising business, operated out of Moscow and specializing in emerging markets.
News Corp is the parent company of FOXNews.com.