Alliance & Leicester has confirmed it is in an "advanced stage" of takeover talks.
The name of a bidder has not been confirmed but is believed to be Abbey-owner Banco Santander - and a price of 299p a share is on the table - valuing the mortgage lender at £1.3 billion.
With a right to receive an interim dividend of 18p a share, the total value of the offer is at 317p a share.
A statement from Alliance & Leicester, however, maintained doubt over the deal.
"There can be no certainty that an offer will be forthcoming or as to its terms," the firm stated.
Speculation is now rife about who the bidder could be with suggestions of a foreign buyer rife.
The BBC reports Abbey-owner Banco Santander has made the offer with the intention of merging the two high street banks.
An announcement from Santander is expected later today.
The current slump in banking stocks in recent months has led to growth in interest in bids for smaller banks.
Gordon Brown has welcomed suggestions of a foreign buyer for Alliance & Leicester.
He told his monthly press briefing: "[A takeover could] benefit the UK economy. We are open to foreign investment in our financial and energy sectors."
The firm's share price rocked on the news, up 51.88 per cent, to 333p at 10:45 BST this morning.