There is growing speculation that Nationwide building society may be considering a bid for the 316 branches being sold by RBS group under EU rules.
RBS was ordered to sell the branches under the terms of the £45 billion bailout it received from the UK government during the financial crisis.
It had planned to sell the branches to Santander, but the deal fell through last week after two years of negotiations.
Initially the branch portfolio was valued at £1.65 billion but it now expected to fetch around £650 million.
If Nationwide does buy the branches it would gain 245,000 small and medium-sized business customers and become a major UK business bank with 1,100 branches, just 100 behind HSBC.
Nationwide announced plans to expand into the small business market in May and has already launched a savings account for business customers and a range of fixed rate bonds.
As a building society, Nationwide will have to ensure that 75 per cent of its loans are secured on residential property.
Other potential bidders include Virgin Money and the private equity firm JC Flowers.
Under European rules, Nationwide must sell the branches by the end of 2013, but RBS chief executive, Stephen Hester, is expected seek an extension to the deadline.
There is also speculation that Mr Hester could seek permission from regulators to call off the sale.
Meanwhile, RBS shareholders have decided to sue the bank’s former chief executive Fred Goodwin for £4 billion, over allegations that he misled them over a £12 billion rights issue in 2008.
The RBS Action Group, which comprises 100 institutions and 12,000 individuals, claims that RBS directors misled shareholders that the rights issue was a capital strengthening exercise when it was really an effort to save the bank from collapse.
As such, they should have been offered them stock at a far lower price.
Investors lost most of their money when the bank was subsequently bailed out by the Government and its share price plunged.