In an interview with the Financial Times, Osborne said "When I say ‘get rid of it’, I mean put it into the good hands of the private sector.”
The Government currently owns 79% of RBS after it bailed out the bank during the financial crisis. To recover the £45bn lent, the government would need to sell the shares at an average of 455p.
However RBS's share prices recently dropped as much as 1.2% following reports of "toxic" mortgage-backed securities sold in the US.
The bank has reportedly set aside £1.9 billion, but it is estimated that the total fine could reach £5 billion.
Earlier in the week, RBS announced plans to cut up to 14,000 investment banking jobs by 2019 as part of a restructure following a profit loss of £3.5bn in 2014.
Last month, Osborne announced that the government sold a further £500m of Lloyds Banking Group shares through the trading plan that was launched in December 2014, taking the total amount of money recovered for the taxpayer from the bank to just under £8bn. The sale reduced the government’s stake in the bank has from around 40% to 24%.
