Santander, Spain's biggest bank, is the sole remaining bidder for the 318 Williams & Glynn branches being offloaded by Royal Bank of Scotland.
The Spanish lender has confirmed it has entered a bid for the branches, speculated to be worth £1.8bn. National Australia Bank and Banco Bilbao Vizcaya Argentaria had previously dropped out of the bidding.
Santander already owns British banks Alliance & Leicester, Abbey and the savings division of Bradford & Bingley.
The RBS branches would "fit like a glove" for Santander, according to Matias Inciarte, a vice-chairman at the lender, Bloomberg reports.
It would mesh very well with Santander's UK strategy of boosting its business with companies, Inciarte added.
RBS is offloading the outlets to comply with a EU ruling after it received more than £45bn in UK Government aid during the credit crunch.
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