Time Warner's board discussed the proposal at length, the people briefed said, and early this month sent a terse letter rejecting the offer, saying that it was better off remaining independent.
Among the points of contention: The stock portion of Fox's offer would be made using nonvoting shares, these people said. Unlike Time Warner, which has no controlling shareholder, Fox is controlled by the Murdoch family and has two tiers of stock, voting and non-voting.
Representatives for Fox and Time Warner could not be immediately reached for comment.
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It is unclear what Fox's next steps will be. With the disclosure of the takeover approach, pressure from Time Warner shareholders could mount on Mr. Bewkes to begin talks. About 70 percent of Time Warner shareholders, including many big mutual funds, also own shares in Fox.
While the talks between Fox and Time Warner have thus far been considered friendly, people involved in the discussions said that Mr. Murdoch is determined to buy Time Warner and is unlikely to walk away.
Mr. Murdoch has been planning the deal with his inner circle: Mr. Carey; his son James; and the company's chief financial officer, John Nallen, people briefed on the matter said.
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Already, a team of Wall Street advisers have been hired on both sides: Fox is being advised by Goldman Sachs and Centerview Partners, while Time Warner has hired Citigroup and other advisers.
For Mr. Murdoch, an acquisition of Time Warner might be a capstone to his long career. People close to him have long said that he sees such a combination as a natural part of a consolidating entertainment industry. Time Warner itself has been part of several of the highest-profile mergers of the past few decades, including the merger of Time and Warner in the 1980s and the disastrous $165 billion sale to America Online at the height of the dot-com boom.
Mr. Murdoch's approach follows Time Warner's spinoff of its legacy print publications, a move that some analysts have said could spur the interest of potential suitors. Beyond Fox, however, it is not clear who would have both the interest and the financial firepower to pursue a deal, though rumors briefly arose that Google was interested in some sort of partnership.
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Mr. Bewkes was asked last week by Variety magazine about speculation that Fox or Google might seek a deal. He replied: "I know nothing about it."
—By CNBC anchor and New York Times reporter Andrew Ross Sorkin