It could move after an Office of Fair Trading probe decided not to order Lloyds to hand over more of its branches after the bank gave 631 of them to TSB.
In an announcement made last night after the stock market closed, Lloyds said it had agreed to boost TSB's profits by £200 million over the next four years by giving it earnings from a £4 billion mortgage portfolio.
Lloyds, owner of Bank of Scotland, will also give TSB £40m to be used to attract more customers. It is likely to be spent on beefing up marketing, product design and improving its network.
Crucially, Lloyds has not been asked to hand over more branches to TSB. This would have been time-consuming for Lloyds staff and the uncertainty caused would almost certainly have led to a delay in the sale of the Government's stake.
The European Commission had given Lloyds until November to sell branches as a condition of its £25bn taxpayer bail-out in 2008.
After last night's settlement, Lloyds and the Treasury will now approach the EC for approval of a new timetable for the flotation of TSB, which is expected in June next year. There is also no impediment to the Government selling the first tranche of shares in Lloyds, which has long been expected this month.
The impact on profits on Lloyds will be miniscule given it is predicted to deliver up to £4bn this year.
The OFT noted that the launch of TSB is "most likely to be felt in Scotland" where the bank has up to 20% of the current account market and 189 branches.