Lloyds Banking Group has stopped exclusive talks with the Co-op on selling 632 branches, along with 5% of the UK's current accounts.
Lloyds was told to make the disposal by the European Commission after it emerged from the financial crisis with a dominant share of UK banking.
The exclusive nature of the talks was always due to be reviewed at this stage, but in recent weeks the Co-op has faced challenges in gaining approval from the City watchdog, the FSA.
Lloyds has also received a new rival bid from NBNK, a banking venture set with the express purpose of taking over the branches.
Lloyds says that the Co-op remains the "preferred buyer", but that it will now proceed with talks with NBNK at the same time.
There has been speculation that the bank would be forced to ask the Commission for an extension of the November 2013 deadline for making the disposal.
But Lloyds maintains that even if the takeover talks fail, it will be able to sell the 632 branches as an independent business, in a public offer of shares on the stockmarket.