Spanish banking giant BBVA is considering a £2bn takeover bid for the British arm of National Australia Bank (NAB), which includes Clydesdale and Yorkshire banks.
Cameron Clyne, chief executive of NAB, is expected to put the banks up for sale within weeks, according to the Sunday Times.
The potential sale comes after NAB failed in its attempt to buy a network of 318 RBS bank branches and is now expected to quit the UK altogether.
Having failed to land the RBS business, which could have transformed the group into one of Britain's biggest banks, NAB is expected to attempt to quit Britain.
Tentative discussions have taken place between BBVA and NAB in recent weeks but it is understood the Spanish bank has yet to make a formal approach, the Sunday Times reports.
NAB has also examined the possibility of listing its UK business, although a sale is believed to be the preferred option.
BBVA has been conducting due diligence on a move into Britain for several months. Santander, its larger rival, has become one of Britain's biggest banks after buying Abbey, Alliance & Leicester and parts of Bradford & Bingley.
Santander is now the only bidder left for the RBS branch network, which will enable it to expand its network further.
The group is considering a £15bn listing of its UK business as a means of funding the RBS acquisition. It would go straight into the FTSE 100 if the float plan proceeds, although analysts believe such a move unlikely because of stock-market volatility.
Two global vehicles
'Further plug advice gap'
Must appoint separate CEOs and boards
Advisers do come out well
Will report to Mark Till