The Financial Times reports Sir Richard Branson and Flowers will bid for the branches after an initial agreement to sell them to Santander fell through.
Brussels set the beleaguered RBS a deadline of the end of next year to sell the branches as a penalty for the bank’s £45bn bail out by the UK government.
Stephen Hester, RBS chief executive, said he believed Brussels would extend the deadline although the FT said Joaquin Almunia, the EU’s competition commissioner, has “consistently argued that RBS and Lloyds Banking Group – Britain’s two part-nationalised banks – have been given plenty of time to comply with their state-aid penalties”.
The deal would see 250,000 small business customers and 1.8m retail savers and borrowers transferred to the winning bidder.
Virgin Money bought Northern Rock at the start of this year and originally bid for the RBS branches, losing out to Santander in 2010.
JC Flowers meanwhile launched British lender One Savings Bank after buying building society Kent Reliance last year.
Flowers is also invested in Castle Trust and is understood to be looking at further investments.
However reports in the Guardian newspaper today suggested that Royal Bank of Scotland may try to keep the 316 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.