The Co-operative Bank, which was put up for sale in February, has received offers from several potential buyers as the troubled lender continues attempts to build up its capital position.
The bank said on Friday that it has received a number of "non-binding proposals" from strategic and financial parties, adding that it has selected "several" of them to enter the next stage of the sale process, during which they will be provided with additional information.
Potential bidders are thought to include Sir Richard Branson's Virgin Money and Clydesdale and Yorkshire banking brands owner CYBG.
But it is thought the sale - set to save the lender from raising up to £750 million or being wound down - could see bidders snap up parts of the bank rather than the whole business.
In a statement, the lender said: "In parallel, the bank continues to have discussions with existing and other potential new investors on options to build capital.
"There can be no certainty that any offer will be made for the bank or as to the level of any proposal or offer that may be made nor that the bank will pursue, or successfully implement, an equity raise and/or a liability management exercise of its outstanding public debt."
It added that the Prudential Regulation Authority has "welcomed the actions being taken".
In March the bank, which has four million customers, said its ability to meet longer-term UK bank regulatory capital requirements has been hampered by low interest rates and higher than anticipated transformation and "conduct remediation" costs.
Co-op Bank almost collapsed in 2013 after the discovery of a £1.5 billion black hole in its finances and it was forced into a painful debt-for-equity swap. As a result, the loss-making lender is now majority controlled by US hedge funds.
The Co-operative Group, which owns just 20% of the bank, fell into the red on Thursday for the first time since 2013 after writing off the value of its stake in the troubled lender.
The mutual slumped to a pre-tax loss of £132 million for 2016 after the value of its holding in the bank was slashed from £185 million in 2015 to zero.