Chancellor George Osborne is understood to be preparing for the sale of up to £2.5 billion of shares within the next few days, aimed at financial institutions such as hedge funds, although the move could be put on hold if there is not enough interest from the City.
The Edinburgh-based lender was the subject of a £45.8bn bailout in 2008, when the government paid around 500p per share for the bank.
As well as providing billions of pounds of emergency loans, the government owns 79 per cent of RBS, a stake worth around £17.3bn.
It is understood that the Treasury is willing to accept a loss on the investment, as RBS shares have been languishing well below the break-even price at around 342p.
Mr Osborne is thought to be prepared for a poor start to the sale in the hope that the share price will be driven up by removing the risk of political intervention.
The Chancellor said in his Mansion House speech to the City in June that the government stands to make a loss of about £7bn if the stake is sold off in one go with RBS shares at their price on 5 June.
But he cited an analysis by investment bank Rothschild finding there would be an overall profit of £14bn if all the government’s remaining shares in all the bailed-out banks were sold.
The move would follow the sell-down of the government’s stake in Lloyds, which was also bailed out by Alistair Darling, the Labour Chancellor behind the plan.
The Lloyds stake has been cut from 43 per cent to just below 19 per cent, with shares above the 73.6p level that the Treasury had paid for them.
The RBS sale has previously been endorsed by the Bank of England governor Mark Carney, who warned that delaying the start of the sale might cost the taxpayer even more.
Meanwhile RBS posted a half-year loss of £153 million last week for the six months to the end of June after setting aside sums for repaying customers and potential legal settlements.
This figure compared to a £1.4bn pre-tax profit in 2014.
Ross McEwan, RBS chief executive, admitted the bank would not be in a position to pay dividends until early 2017 as restructuring costs and litigation payments had taken its toll on its recovery.
The lender put aside £1.3bn for potential legal settlements for misconduct, of which £459m was taken in the second quarter.
In May, RBS and the Japanese bank Nomura were ordered to pay $806m (£516m) together for making false statements when selling mortgage-backed bonds to US agencies Fannie Mae and Freddie Mac.
RBS has already paid £399m in fines to the US and UK regulators over the scandal of rigging foreign exchange markets.
However, things looked brighter for the bank towards the end of June when its net profit rose unexpectedly by 27 per cent to £293m for the three months to the end of June.
The Chancellor announced his plans to sell the government’s stake in bank back to private investors in June, while a retail sale of the government’s remaining stake in Lloyds bank is earmarked for next year.
In his annual Mansion House speech to the City, Mr Osborne told traders: “In the coming months we will begin to sell our stake in RBS.
“It’s the right thing to do for British businesses and British taxpayers.
“Yes, we may get a lower price than Labour paid for it. But the longer we wait, the higher the price the whole economy will pay.
“And when you take the banks in total, we’re making sure taxpayers get back billions more than they were forced to put in.
“From bailing out the banks to bringing them back from the brink, now is the time for RBS to rebuild itself as a commercial bank no longer reliant on the state but serving the working people of Britain.”
The Treasury declined to comment last night on the potential sale.
A spokesman for RBS said it was up to the UK government to decide when to start selling down the taxpayer’s stake in the lender.