Although the Royal Bank of Scotland-led (RBS) consortium did not raise its offer from the $97.9 billion it initially offered it has upped the level of the cash in the deal from 79 per cent to 93 per cent.
The remainder of the offer from the consortium, which includes Spanish bank Santander and Belgian Dutch firm Fortis, is to be made of RBS shares.
News of the revamped offer follows Dutch regulatory authorities' decision to permit the sale of ABN Amro's La Salle unit to Bank of America for $21 billion.
RBS has planned to buy La Salle, but under the terms of the new deal will receive money from its sale.
The new offer is still considerably higher than that proposed by Barclays Bank, which has tabled a rival bid of $88 billion.
Either deal would represent the largest-ever cross-border European banking transaction.
Barclays is now expected to increase its offer, finding increased synergies from any merger to justify a higher price tag.