The reports come after NAB, which owns the Yorkshire and Clydesdale banks, announced it was dropping its bid to buy more than 300 Royal Bank of Scotland branches.
According to analysts, NAB’s UK business is worth about £2bn.
It is believed the Australian bank is looking to quit the UK after its failure to buy the RBS branches, which would have made it one of the UK’s biggest high street banks.
Santander is said to be the only remaining contender to buy the branches.
If its bid proves successful, it would provide a further boost to Santander’s UK branch network following the acquisition of Bradford & Bingley and Alliance & Leicester branches last year.
It would also increase the Spanish financial services firm’s business banking operation.
Santander is believed to be considering a listing of its UK business to fund the RBS branch acquisition.