MILAN, Jan 8 (Reuters) - Italy"s fifth-largest bank BPER Banca (EMII.MI)is preparing to improve its offer for ailing peer Carige (CRGI.MI)to prevail over rival suitor Credit Agricole Italia (CAGR.PA), two sources close to the matter said. Before Christmas, BPER had offered a token 1 euro for Carige and demanded a 1 billion euro ($1.1 billion) capital injection from the depositor protection fund (FITD) that owns the Genoa-based lender following a 2019 industry-financed bailout. read more That sum exceeded the 700 million euros the FITD, which is financed by Italian banks, was allowed to spend based on the previous year"s contributions by members. After the fund rejected BPER"s initial offer, the Italian arm of France"s Credit Agricole filed its own proposal for Carige requesting a lower capital injection, sources had previously told Reuters. However, BPER remained the favoured bidder with Italian institutions keen to see the country"s mid-tier lenders bulk up and some FITD members wary of further expansion by Credit Agricole Italia which last year acquired small regional bank Creval for 1 billion euros. BPER"s board is set to approve before Monday a new proposal for Carige with a downsized capital request, the two sources said. BPER declined to comment. Daily Il Messagero reported on Saturday BPER would ask for just 600 million euros from FITD. The fund, which owns 80% of Carige after spending 600 million euros to rescue it, on Thursday said its steering committee was expected to select a bidder at a meeting on Monday to enter exclusive negotiations . read more To ease a sale of Carige and solve a long-standing banking headache, Rome has lined up tax incentives worth some 400 million euros. Carige has been hunting for a buyer since Cassa Centrale Banca (CCB), which had taken an 8.3% stake as part of the 2019 rescue, last year walked away from a proposed acquisition. The buyer of the combined 88.3% stake held by FITD and CCB would then buy out remaining investors in Carige, a prospect which has sent its shares up by nearly a third since mid-December when news of BPER"s interest first emerged. ($1 = 0.8804 euros)