Time Warner's board rejected Murdoch's $80 billion takeover offer earlier this month, but the Fox chairman and chief executive officer is expected to continue the pursuit.
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Bloomberg said the offer of board seats as part of an increased bid could help allay concerns of Time Warner investors about the dual-class stock structure that gives control to Murdoch, 83, and his family.
Nathaniel Brown, a spokesman for New York-based Fox, and Keith Cocozza, a spokesman for Time Warner, declined to comment on whether the companies have discussed board seats, Bloomberg said.
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Mario Gabelli, one of Time Warner's longest standing shareholders, said in an interview with Bloomberg last week that Murdoch should offer Time Warner investors a couple of board seats.
In a deal announced Friday, Britain's BSkyB agreed to pay $9 billion to buy Murdoch's pay-TV companies in Germany and Italy. Fox is expected to use the proceeds to fuel its pursuit of Time Warner.