According to the Financial Times, British chancellor George Osborne is mulling over the prospect of inviting bids for the government's Â£46 billion ($73.1 billion) holding in the company, which was nationalised at the height of the 2008 financial crisis.
It is understood that any deal will be subject to the findings of the Independent Commission on Banking (ICB), which is currently chaired by former Barclays boss Sir John Vickers and is examining the universal banking model.
The ICB is expected to set preliminary terms for a possible sale of RBS and rival Lloyds. However, should the panel opt to separate retail banks from investment operations, there has been speculation that the overall value of RBS could take a hit.
"Once the uncertainty around the [ICB] has been removed, I don't see any reason why a sale should not take place," an anonymous RBS insider told the newspaper.
Bosses at the bank are hopeful that it will return to profitability in the current financial year and there is understood to be some confidence that market conditions will be favourable for a sale, with an initial chunk worth around Â£5 billion to be offered to potential buyers.
Sources close to Mr Osborne agreed that a privatisation was a possibility in 2012, but insisted the Conservative minister would not be rushed into any final decision and suggested the latest reports may be a kite-flying exercise by RBS bosses looking to break away from state control.
Last week, Sir David Cooksey, the chairman of UK Financial Investments - which manages government stakes in RBS and Lloyds - warned against splitting the financial institutions for fear it could damage the worth of public holdings.
By Tony Aynsley