Lloyds has signalled to investors it may take up an option to "upsize", the sources said.
The shares are expected to list at around the midpoint of the revised 250p to 270p price range set by the bank, after decent demand.
A 260p issue price would value TSB at about 0.8 times its book value or £1.3 billion.
Lloyds said in its prospectus it planned to sell 125 million shares in TSB, or a 25 per cent stake, but strong demand could prompt the release of a further 50 million shares to float 35 per cent.
TSB has around 4.5 million customers and six per cent of branches across the UK, making it the seventh-largest retail bank in the sector.