Chancellor George Osborne has received the green light to begin selling £600 million of shares in the Royal Bank of Scotland, representing just under 5.2% of its overall stake in the bank.
UK Financial Investments (UKFI), through which the Treasury owns its stake in RBS, has told the Chancellor it would be "appropriate" to conduct the first sale of the Government's shareholding.
It will reduce the Treasury's overall holding in RBS from 78.3% to 73.2%.
An HM Treasury spokesman said: "The Government set out its objectives for its shareholdings in the banks in the Chancellor's annual Mansion House speech in June 2013 - getting the best value for the taxpayer, maximising support for the economy and restoring them to private ownership - and as set out in that address, the Government will only conclude a sale if these objectives are met.
"In his Mansion House speech in June this year, the Chancellor announced his intention to start returning RBS to the private sector in the coming months, following advice from the governor of the Bank of England."
The Government paid about 500p a share for the bank, compared with the current price of about 339p.
UKFI plans to sell about three-quarters of its holding in RBS by the end of the current five-year parliament.
A previous report by investment bank Rothschild said that, if all of the Government's stake was sold at current prices, the taxpayer would lose around £7 billion.
However, UKFI estimates that the RBS share price will rise as the firm returns to health and more stock is sold to the market.
Elsewhere, the Government confirmed it has sold a further 1% stake in Lloyds Banking Group, reducing its total holdings to 13.99%.
In a stock market disclosure, the Treasury said it has recouped £14 billion from the sell-off, all of which has gone towards reducing the national debt.
The price for the share sale, which was conducted on Friday, was not disclosed.
During the financial crisis, the government bought a 41% stake in Lloyds worth around £20.5 billion.