Sources close to the putative deal have indicated that UnionBanCal is considering a price of $73-$73.50 per share to sell the remaining 35 per cent of stock to the bank.
This is a significant improvement over Mitsubishi UFJ's offer last week, which equated to $63 per share - and higher still on its previous bid earlier this year at $58.
In total, the new offer values the UnionBanCal at $3.5 billion.
Rejecting last week's bid, the US lender said that the deal was "not in the best interest" of some shareholders, and was made at a time in which there was "negative sentiment in, and [an] uncertain outlook for, the overall banking sector".
On Friday, UnionBanCal stock closed at $65.49 in New York.