TOKYO (Reuters) - U.S. private equity firm KKR will raise its tender offer price for Japanese IT company Fuji Soft to 9,850 yen a share from 9,451 yen, above Bain Capital's rival offer of 9,600 yen, a person familiar with the deal said on Tuesday.

The person declined to be identified because the information is not yet public.

KKR and Bain are trying to buy Fuji Soft in competing tender offer bids worth as much as $2 billion.

KKR now has a 34% stake in Fuji Soft after the first stage of a two-part bid, but has failed so far to amass a majority due to Bain's higher offer. It has repeatedly extended the tender offer period, with the latest due to end on Friday.

Fuji Soft's shares were up 1.53% at 9,950 yen in early afternoon trade.

Bain, which is supported by Fuji Soft's founding family, has not launched its tender offer bid yet, having said that it would wait for KKR's bid to fail or be withdrawn.

KKR had initially offered 8,800 yen a share for Fuji Soft last August. Bain announced its rival offer the following month, at 9,450 yen, prompting KKR to raise its offer to 9,451 yen. It had kept its offer price there despite Bain's re-raising its offer to 9,600 yen.

KKR will announce the latest change as early as on Tuesday afternoon, the Nikkei business daily reported earlier.