At least 10% of its stock is likely to be sold at the end of 2014, which could raise £5billion for the Government ahead of a 2015 poll, according to reports.
It would be the first return of cash to the taxpayer since the Government spent £45.5bn bailing out the lender after the financial crisis in 2008.
RBS declined to comment, but the report comes amid further pressure on Chancellor George Osborne to reduce Government debt after ratings agency Moody's cut the UK's credit rating to AA1 on Friday.
There has been political pressure for RBS to go back to the private sector, with Prime Minister David Cameron urging bosses to strengthen the company quicker in preparation.
Taxpayers are still sitting on a paper loss of £14bn as shares remain below the £5 break-even price paid by the Government.
The lender will announce its full year results on Thursday, and banking analyst Ian Gordon at Investec Securities is expecting compensation provisions for mis-selling to plunge RBS even deeper into the red, with losses of £3.9bn in 2012 – far worse than the £766 million loss reported for 2011.
RBS, 81% owned by the state, was fined £390m by US and UK regulators this month after evidence of traders fixing the Libor interbank lending rate.
A report yesterday suggested RBS will also announce £30bn cuts to its investment banking arm and hundreds of job cuts.