The Co-operative Bank has confirmed weekend reports that it wants to buy TSB from Spanish lender Banco de Sabadell.
No discussions are currently underway but the Co-op said it had sent a letter to the TSB owner expressing its interest.
Sabadell said on Saturday its board has rejected an offer from Co-operative Bank for TSB
A Sabadell spokesman said: "This is not a transaction that we wish to explore at this moment, as we have previously expressed publicly."
Sky News reported the offer was in the region of £1bn.
Both banks are relatively small players in the UK bank sector with around eight million customers combined, which is more than Virgin Money though it has a larger loan book.
Co-op tried to buy TSB’s in 2013 when Lloyds Bank was trying to sell them but its attempt collapsed when the bank was hit by a string of scandals and financial problems culminating in its being rescued twice.
TSB meanwhile has been plagued with IT issues since it was split out from Lloyds and acquired by the Spanish bank in 2015.
Sky said the Co-op’s approach is likely to spark interest from other suitors in TSB, which currently has 300 branches.
Last week, Sainsbury’s dropped plans to sell its bank to US private equity firm Centerbridge after the two failed to agree on a price.
Co-op meanwhile failed to conclude a deal with another US private equity firm, Cerberus, in December.