Royal Bank of Scotland is expected to indicate this week that the Government will begin to sell off its stake in the group before the end of the year.
Stephen Hester, chief executive of the bank in which the taxpayer has an 83% holding, is expected to say the group is on the road to recovery when he unveils its annual results on Thursday, paving the way for a sale of the Government's shares, according to the Sunday Times.
RBS is still expected to be in the red, with analysts predicting a pre-tax loss of £613 million for 2010, but this is a marked improvement on the £3.6 billion loss recorded for the previous year.
The group is also expected to write off another £9 billion in bad debt as a result of its exposure to the troubled Irish economy through its Ulster Bank subsidiary, although this too is down on the £13.9 billion it wrote off in 2009.
It is thought that UK Financial Investments (UKFI), the government body that looks after taxpayers' interests in the part-nationalised banks, will try to sell a small part of its holding later this year on the back of the improved result.
It has been suggested that it may try to offload small parcels of the bank's shares at a low price to test market appetite for the stock. Selling just a 5% stake in the group at the current share price of 48.53p would bring in £1.4 billion for the Treasury.
But UKFI has to sell the holding at more than 50p a share if the Government is to make a profit from the bail-out of the bank.
RBS and fellow part-nationalised bank Lloyds Banking Group are both thought to have held meetings with sovereign wealth funds in recent months in a bid to drum up interest in their shares.
But it is thought that any sale of the Government's stake could be difficult to achieve until Sir John Vickers, chairman of the Independent Commission on Banking, has produced his final report on whether the UK's banks should be broken up. His initial report is due in April.