Following the collapse of a £1.65bn deal to sell the network to Santander UK, Nationwide is the latest company to show interest in purchasing the assets which also includes 40 bank centres for small and medium-sized businesses.
Virgin Money and private equity firm J C Flowers have both been linked to the RBS purchase.
A source close to Nationwide told The Sunday Times: “We are watching the situation with interest.”
RBS, which has a network of 1.8m retail customers and 250,000 small business customers, is being forced to sell these assets as a condition of its £45.5bn government bailout.
However reports in the Guardian newspaper earlier in the month suggested that Royal Bank of Scotland may try to keep its branches.
RBS indicated to the paper that it might argue it should be able to keep the branches now that the UK retail banking market is already open to more competition at a time when the economy has deteriorated.
"The commission has been much more flexible. It used to be a pretty severe regime but they are making different judgments," said a spokesman for RBS
