The Co-operative Group has said it will put in a renewed bid for 632 branches being sold by Lloyds Banking Group.
The Co-op will next week submit a second round offer for the estate and £36bn (€41.8bn) of assets, which Lloyds has been ordered to sell in order to meet European competition rules.
NBNK Investments, a takeover vehicle run by former Northern Rock boss Gary Hoffman, has already said it has put in a bid.
Other interested parties are believed to include American investment firm Sun Capital, Virgin Money, the bank arm of Sir Richard Branson's Virgin Group and National Australia Bank.
However, Lloyds has not ruled out floating the business - dubbed Project Verde - on the stock market if it does not attract enough interest.
Co-op chief executive Peter Marks said: "We have a clear strategy for driving The Co-operative Group forwards. As part of this we remain interested in the Lloyds Banking Group's branch assets as we believe this would support our moves to grow our relationship banking business in the UK."
Lloyds, which is 41% owned by the taxpayer, this week was rocked after its chief executive, Antonio Horta-Osorio, went on sick leave. The bank said it is confident he will be back before the end of the year.
Lloyds is being forced to divest the branches by the European Union in return for the £20bn (€23.23bn) in state aid it received following the 2008 credit crisis.