Industry insiders predicted the move by the part-taxpayer owned bank after the UK Government urged the Edinburgh-based institution to speed up the overhaul of the business.
They suggest RBS is drawing up proposals to sell a 20% stake in the branch network to one or more outside investors before trying to list the business on the stock market.
In 2008, the UK Government saved the Scottish bank by injecting £46 billion into it in the costliest ever bailout.
Stephen Hester, the chief executive brought in to turn the finance house around, has undertaken major restructuring, including the axing of 36,000 jobs, but has yet to return it to profit and must, to comply with EU state aid rules, sell 316 branches by 2014; most of them are in England.
Bidders reportedly expect to be told about RBS's preferred option for disposing of the network at around the time the bank reports its full-year results next week.
Last autumn, RBS had lined up the sale of the branches to Santander UK but the deal fell through amid recriminations over computer systems.
Conservative Party sources have pointed out how George Osborne saw continued ownership of RBS as politically untenable in the wake of the Libor-fixing and other scandals and that the Chancellor was keen to end the state's role soon.
The UK Government played down suggestions it was preparing to dispose of its 82% stake in RBS in a pre-election share giveaway to voters, but David Cameron made clear he was "keen to examine all possibilities" for returning the bank to the private sector.
Asked whether the Government was planning a give-away, the Prime Minister replied: "These are all interesting questions for the future. The first job is to turn around the performance of RBS and to strengthen its balance sheet, strengthen its business and that's what Stephen Hester and his team are doing."
The state-owned bank could be ready for privatisation this year but at present prices that would result in a huge loss to the taxpayer.
The Liberal Democrats have championed the idea of a share give-away and it was reported at the weekend that Conservative ministers were now also looking at the idea of handing the money back to taxpayers in the form of shares. These could be worth up to £400 per household.
Meanwhile, Lloyds Banking Group was fined £4.3 million by the City watchdog after up to 140,000 customers had their payment protection insurance compensation payments delayed.
The customers were not paid redress within 28 days of receiving a decision letter and almost 9000 had to wait more than six months for their compensation, the Financial Services Authority said. The failings relate to Lloyds TSB Bank, Lloyds TSB Scotland and Bank of Scotland, leading to a total fine of £4.3m.
The regulator said it had imposed a large fine because Lloyds' redress payments systems fell "way below the standard the FSA expects".