According to a report by the BBC, the government, which controls 82% of the bank, has been negotiating with Abu Dhabi sovereign wealth funds for months.
The report states the government could sell up to a third of its stake to Abu Dhabi, one of the seven states of the United Arab Emirates.
It also suggests the sale is likely to be loss-making, as RBS shares currently trade at much less than the 50p the government paid in 2008.
RBS shares currently trade at 27p, meaning taxpayers could suffer losses of around £1bn for every £1bn paid by the government.
In 2008-09, the government bailed-out RBS with £45.4bn of taxpayers’ money, to prevent it from collapsing following its near-ruinous acquisition of ABN Amro.