The reprivatisation of Lloyds Banking Group could be completed by the government in 2014.
A 33 per cent share in the company is retained by the government following its bailout during the recession, with the stake currently worth around £18.4 billion.
The Daily Telegraph reports that the remaining shares may be sold off by the end of the year.
"Post-results is when a further institutional offering would make most sense. After that, the thinking is [that] an autumn sale, combining an institutional and a retail segment, is a realistic prospect," said one source.
Recent research carried out by the National Audit Office (NAO) showed that the previous share sale of Lloyds Banking Group cost the taxpayer as much as £230 million.
Despite this, the NAO head Amyas Morse argued that the timing of the share sale by the government was correct.
A spokesperson from the Treasury refused to give details about the government's plans, insisting it "will sell further stakes in Lloyds when it is in taxpayers' interest to do so".
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