By Miho Uranaka, Makiko Yamazaki and Ritsuko Shimizu

TOKYO (Reuters) -Private equity firms KKR (KKR) and Bain Capital (BCSF) each offered more than $5 billion in first-round bids for the non-core assets of Japan's Seven & i Holdings, according to people familiar with the matter.

KKR offered around 800 billion yen ($5.1 billion) for York Holdings, an entity due to be spun out of the Japanese retailer, two of the people said. Rival U.S. firm Bain offered around 1.2 trillion yen, one person said. Local buyout firm Japan Industrial Partners offered around 750 billion yen, one said.

All three firms were successful in the first round of bids for the assets, according to two of the people. Reuters spoke to three people about the first-round bids, all of whom declined to be identified because the information hasn't been made public. The size of the bids has not previously been reported.

The bids exceed the 500 billion yen enterprise value - a measure that includes debt - that the 7-Eleven owner had expected, according to one of the people.

A spokesperson for Seven & i declined to comment, saying the bidding process was not public. KKR, Bain and Japan Industrial Partners also declined to comment.

Seven & i is looking to hive off non-core businesses, including its sprawling supermarket operations, into the York Holdings unit, which will house 31 subsidiaries including the group's superstores business, baby goods store Akachan Honpo and the company that operates Denny's restaurants in Japan.

Separately, the retailer's founding family is in talks to take Seven & i private. That deal, a management buyout, is designed to fend off a $47 billion takeover offer from Canada's Alimentation Couche-Tard.

The three private equity firms will now submit legally binding proposals but may alter their offers following due diligence, two of the people said. Unsuccessful bidders from the first round could still enter negotiations if the three fail to reach an agreement with Seven & i, two of the people said.

Seven & i is aiming to select the winning bid as early as February, one person said. The decision would then be finalised by the spring, another person said.

The founding family has also approached Bain and KKR about mezzanine funding for the management buyout, two of the people said.

Seven & i's market capitalisation stood at 6.2 trillion yen as of Dec. 24. The privatisation, if realised, would be the largest ever of a Japanese firm.

($1 = 157.0300 yen)

(Reporting by Miho Uranaka, Makiko Yamazaki and Ritsuko Shimizu; Writing by Anton Bridge; Editing by David Dolan and Edmund Klamann)