Lloyds Banking Group confirmed this morning Co-Operative Bank and NBNK Investments are the last two bidders in the running for its 632 branches and retail assets.
A bid from Sun Capital was not taken any further, according to the BBC.
Co-Operative Bank declined to comment further at this stage of the bid, however, the considerable assets would boost its profile and lending capacity on the high street as a mortgage lender and current account-holder.
Lloyds, part-owned by the government, has been forced to sell off the branches, following a ruling targeted to meet European Commission competition rules.
The group will also continue to work on an Initial Public Offering as a potential alternative to a direct sale, it confirmed.
Tim Tookey, Lloyds' interim chief executive, due to leave the bank for another job in February, said: "We are very pleased with the level of interest and detail of the offers that have been made. We will now move quickly in parallel talks with each bidder."
Lloyds' chief executive Antonio Horta-Osorio has been off work on stress-related sick leave since early November after being told by doctors that he should rest.
Lloyds appointed an interim group CEO on Monday this week to succeed Tookey, David Roberts, in case Osorio's sick leave is extended.
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