Lloyds says its preferred option for the sale of 630 retail branches is to sell them to the Co-operative Group.
The mutually-owned Co-op had been in competition with new bank venture NBNK for the assets.
Lloyds will now enter exclusive talks with the Co-op, which runs a financial services division along with a supermarket retail arm.
It comes as the bank said boss Antonio Horta-Osorio is to return to work from sick leave on 9 January.
Taking over the Lloyds retail branches would give the Co-op the chance to become Britain's seventh-biggest bank.
It is hoped that a deal will be concluded by the end of the first quarter in 2012.
Lloyds is 41%-owned by the UK taxpayer,