TOKYO, Dec 11 (Reuters) - U.S. private equity firm Bain

Capital is set to raise its offer price for Japan's Fuji Soft

to 9,600 yen ($63.35) per share, the Nikkei newspaper

reported on Wednesday, trumping a recently increased tender

offer bid from rival KKR.

The increased offer price, at a 1.6% premium to KKR's 9,451

yen a share bid, would mark the latest salvo in the running

battle between the two private equity giants over the $4 billion

software maker.

The scramble for Fuji Soft has helped illustrate Japan's

growing prominence as a hotspot for deals, including rising

demand from private equity firms.

In the first 10 months of this year, Japan saw a record $81

billion in inbound M&A, up 17-fold from the same period last

year, LSEG data shows.

KKR increased its tender offer price to 9,451 yen per share

last month, up from its original bid of 8,800 yen.

($1 = 151.5400 yen)