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One proposal under discussion would value at around $6 billion - $10 billion and would give News Corp a more than 20% stake in the combined company, according to the Wall Street Journal.

Murdoch has held on/off discussions with Yahoo over the past year. Responding to questions, Murdoch told analysts and reporters on a conference call last week that his company was not interested in bidding for or pursuing any transaction with Yahoo.

Analysts say that News Corp is unlikely to better Microsoft's offer. "It is hard to imagine that Rupert would be willing to put enough cash in the deal to make it interesting to Yahoo shareholders," says RBC Capital Jordan Rohan.

News Corp declined to comment. A Yahoo spokeswoman also declined comment on the report and reiterated the company's position that its board of directors continues to explore its options.