While that offer, to TSB’s Spanish owner Sabadell was rejected, others now seem possible.
With the big banks again making big profits, but cutting branches, reasons for the second-tier lenders to unite seem to grow, say analysts.
Low interest rates have hit margins and a new breed of app-based banking has taken away at least some custom.
Sabadell said “this is not a transaction that we wish to explore at this moment”. The deal was put at £1 billion.
Nick Slape, CEO of the Bank said: “Our unique brand, underpinned by co-operative values and ethics and the significant progress we have made in returning our Bank to profitability is a testament to the hard work of our colleagues and the loyalty of our customers - which we continue to place at the heart of all our decisions.”