The sale of shares in NatWest to the general public could happen as early as June, UK Government Investments (UKGI) has confirmed.
The Treasury still owns 39% of the bank since it bailed it out to the tune of £46bn during the 2008 financial crisis.
But UKGI, the company responsible for government investments, has been exploring a share sale since the chancellor announced plans last year.
Jeremy Hunt has said any sale would need to achieve "full value for money".
On Tuesday, Holger Vieten, who is in charge of selling the governmentʼs shares in NatWest, told MPs on the Treasury Select Committee that the process "potentially could happen" as early as June.
"The very earliest could be around summer time, but we donʼt have an exact date," the UKGI director said.
Since NatWest, previously known as Royal Bank of Scotland, was bailed out in 2008, the government has been gradually reducing its shareholding in the bank.
It said early in 2023 that it wanted to sell its remaining stake in the bank by 2025 or 2026 and in his Autumn Statement in November Mr Hunt said options would be explored during the 12 months that followed.
The chancellor referenced the 1986 "Tell Sid" advertising campaign, in which characters urged each other to "tell Sid" about the chance to buy shares in British Gas.
The move prompted hundreds of thousands of people to buy shares in the energy firm, one of several companies privatised under former Prime Minister Margaret Thatcher in the 1980s.
Mr Vieten said UKGI had hired advisers, including legal and banking experts, to work out options for a share sale before a proposal would be presented to ministers to decide on.
He said there were several "windows" for a retail offer, but added the company had not come to any firm conclusions.
"Itʼs very much a work in progress," he said.
MPs also raised the fact that NatWest has still not appointed a permanent chief executive following the high-profile resignation of Dame Alison Rose after a row over the closure of former UKIP leader Nigel Farageʼs bank account.
Dame Alison quit in July last year after admitting she made a mistake in speaking about Mr Farageʼs relationship with the bank, and her successor Paul Thwaite was only handed the reins for an initial 12-month period.
"I think they need to provide clarity to the market on their proposals around either confirming the interim chief executiveor a process around appointing a permanent chief executive for the market to be comfortable," said Charles Donald, chief executive of UKGI.
Richard Haythornthwaite is also to succeed Sir Howard Davies as NatWest Group chairman in April.