The British government is preparing to sell its 39% stake in Lloyds Bank to private investors.
Chancellor George Osborne said Lloyds was in a good position and investor interest was growing.
Lloyds is already planning to float 631 branches under the TSB brand at some point next year.
A deal for the branches to be bought by the Co-op Bank fell through in April.
The BBC's business editor said the chancellor has decided that the initial tranche would be sold to investment institutions rather than retail investors, as an institutional placement is likely to be the most effective way of managing risk and getting value.
The Banking Standards Commission said earlier on Wednesday that Lloyds was better placed to return to the private sector and that RBS could be split into two. Taxpayers have an 81% stake in RBS.
Mr Osborne said he would look at whether to split the good bits (of RBS) from the bad. He said he did not want "a quick sale of our RBS shares".
Earlier, the Banking Standards Commission said the continued ownership of RBS by the government, "created serious problems for the UK economy".
The commission said it was time to look afresh at the timetable for returning RBS to the private sector.
