(Reuters) - Investment firms Knighthead Capital Management and Certares Management sweetened their bid to fund Hertz Global’s exit from bankruptcy, valuing the U.S. car rental firm at $6.2 billion, the Wall Street Journal reported on Friday. Knighthead and Certares have proposed taking control of Hertz with backing from some existing shareholders of the rental firm and private-equity company Apollo Global Management Inc, which has agreed to supply up to $2.5 billion in preferred equity financing, the report said here, citing people familiar with the matter. Last month, Knighthead and Certares agreed to buy a majority stake in Hertz for $4.2 billion to help it ride out of bankruptcy by early- to mid-summer. But their offer was eclipsed by a rival bid earlier this month by private investment firms Centerbridge Partners, Warburg Pincus and Dundon Capital Partners. The proposal, backed by Centerbridge Partners, Warburg Pincus and Dundon Capital Partners, was supported by holders of more than 85% of Hertz’s unsecured notes. Hertz, Knighthead and Certares were not immediately available for comment.