The Treasury could begin the process of selling part of the government's stake in Royal Bank of Scotland from Monday, according to BBC sources.
UK Financial Investments, through which the Treasury owns its four-fifths holding in RBS, may sell a stake worth billions of pounds, should there be enough appetite among City investors.
The move is tentative, and could be set back a month or more.
The Treasury and RBS declined to comment.
The first task would be choosing investment banks to manage the sale. The coming week is seen as a good time to attempt a sale before holidays start in earnest among investors.
Should there be too little interest, a sale could be attempted again from September, the BBC understands.
Chancellor George Osborne announced in June his plan to sell the bank back to private investors.
The government provided RBS with a £45.5bn bailout in 2008.
The government paid about 500p a share for the bank, compared with the current price of about 342p.
RBS reported a half-year loss of £153m last week after setting aside more money for repaying customers and potential legal settlements.
But the bank's net profit rose to £293m for the three months to the end of June.
