Nationwide Building Society is considering making a bid for the 316 branches that Royal Bank of Scotland was due to sell to Santander, it was reported.
The mutual is looking at an offer as speculation mounts over which firms will bid following the collapse of the deal with Spanish-owned Santander UK, according to The Sunday Times.
RBS had planned to sell the assets, which feature 316 branches and 40 banking centres for small and medium-sized businesses, to Santander in a deal approved by the European Commission as a condition of receiving state aid.
Santander agreed in August 2010 to buy the assets, but it pulled out earlier this month as it became apparent a revised target for the purchase to be completed by the end of the year would not be achieved, with the group also blaming the complexity of RBS's technology platform.
Virgin Money has also been linked to a bid for RBS branches that were due to be sold to Santander. The Sir Richard Branson-backed bank, which took control of nationalised Northern Rock in January, was said to have been "very keen" on the business when it was up for sale in 2010 and has reportedly expressed an interest in re-bidding.
Other potential suitors are thought to include US private equity firm JC Flowers and buyout firm NBNK.
Nationwide was not immediately available for comment.
Santander is likely to face questions over its decision to withdraw from the deal when it reports third quarter figures on Thursday.
RBS chief executive Stephen Hester promised there would be "no disruption" for customers and said the taxpayer-backed bank would begin a process to seek a new buyer, having already laid the ground work for transfer of the branches to a new owner.
State-backed RBS is also reportedly planning to spend £80m on upgrading its computer systems following the embarrassing glitch in June that caused disruption to 12 million business and personal customers.