Lloyds Banking Group may be fully privatised within 18 months as the UK government reportedly sets to work on selling off its remaining stake.
Lloyds is 32.7% owned by British taxpayers following a multi-billion pound bailout during the financial crisis that spared it from collapse.
A 6% stake sale by the government in September was hailed a value-for-money success by the National Audit Office (NAO), a public finances watchdog, despite the taxpayer losing £230m in the deal.
The government said after its September stake sale it would not release any more of its holdings for three months.
According to Reuters, the government and UK Financial Investments (UKFI), the public body which manages taxpayers' stakes in Lloyds and fellow bailed-out institution Royal Bank of Scotland (RBS), are assessing how best to sell off the rest of the Lloyds holding now the three-month no-sale period has passed.
The remaining stake will likely be sold off in tranches with the next batch probably shifted to institutions, though a retail offer has not been ruled out.
The NAO's assessment of the Lloyds stake sale said the £230m loss should be seen as a small price for securing financial stability during the crisis, rather than a failure of the current sale process.
"The programme of sales of the taxpayers' holdings of bank shares has got off to a good start. Sale options were reviewed thoroughly and UKFI looks to have got its timing right," said Amyas Morse, head of the NAO.
"The sale took place when the shares were trading close to a 12-month high and at the upper end of estimates for the fair value of the business. Furthermore, the share price in trading after the sale has remained steady."
Lloyds has returned to profitability, though it has been hit by billions in litigation and compensation costs relating to past misbehaviour, such as the mis-selling of financial products.
In October, it added another £750m to is payment protection insurance (PPI) mis-selling compensation pot, taking the total to £8bn.
RBS, in which the UK government holds an 81% stake, has also been repeatedly hit with litigation and compensation costs. It has been heavily involved in both the mis-selling and rate fixing scandals.
The bank's share price trades well below the levels at which it was bailed out by taxpayers. Chancellor George Osborne ruled out any RBS sell off before the 2015 general election.