Lloyds Banking Group is reportedly mulling a cut-price sale of the 632 bank branches it has to offload as a penalty for receiving state aid.
The Project Verde business was expected to fetch between £1.5 billion and £2 billion last year but with bank shares under pressure market sources told the Sunday Times it may be willing to lower the price by as much as 50%.
Lloyds has promised an update on the sale by the end of June, with Co-op its preferred option despite regulatory hurdles delaying the sale process.
The part-nationalised bank group has until November 2013 to dispose of the Verde estate, which accounts for a 4.6% share of the UK current account market and up to 19% of Lloyds' mortgage book, with around five million customers.
The Co-op, which is Britain's biggest mutually-owned business, will triple the size of its banking business if the deal goes ahead.
Lloyds, which is due to hold a board meeting on Wednesday, could also attempt a stock market listing or consider a deal with NBNK, the bank buy-out vehicle which is waiting in the wings.
Some of the regulatory uncertainty surrounding the Co-op offer has been addressed through plans for Verde's management team to transfer with the business in order to run the Co-op's enlarged banking arm.
Lloyds will also provide the systems and technology platforms needed to run a large banking operation.
However, there is still concern that because the financial services arm will dwarf the rest of the Co-op business the whole of the Co-op will have to be regulated as a financial institution.
It is not clear whether monitoring of this kind will meet with the approval of the Co-op board, which is a group of elected member representatives and customers.