George Osborne is reportedly expected to set out plans to start selling off the taxpayer stake in Royal Bank of Scotland in his Mansion House speech next week.
The Chancellor will expand on remarks in January when he said the government was "close" to the point where it could start returning RBS - 79% owned by the taxpayer - to the private sector, according to newspapers.
It comes a day after the Treasury extended its latest trading plan to dispose of its holding in Lloyds Banking Group and confirmed that a "Tell Sid"-style offer of Lloyds stock to retail investors will be launched in the next 12 months.
Both groups were rescued by the government at the height of the financial crisis, with £20 billion poured into Lloyds and £45 billion into RBS.
The Lloyds stake has been cut from 43% to just below 19%, with shares above the 73.6p level that the Treasury had paid for them.
But RBS has been languishing well below the break-even price of around £5 per share and last night closed at 341.4p.
However, Mr Osborne is thought to be prepared to start the sell-off at a loss in the hope that it drives the share price up by removing the risk of political intervention, the Times reported.
The reports about next Wednesday's speech come after the Chancellor said in January: "Early in the next Parliament we will have to make a decision on the timing of any exit programme from RBS."
The Treasury and RBS both declined to comment.
Chief executive Ross McEwan has previously stressed that the timing of a shares sale would be a matter for the Government, as he strives to simplify the business and make it a more UK-focused lender centred on retail and commercial banking.