mortgage bank Halifax is in merger talks with the Bank of Scotland.
In a brief statement, the pair said they were in discussions over a "potential merger of equals".
The talks come just weeks after Bank of Scotland's hopes of a tie-up with Abbey National were scuppered by Lloyds' takeover interest in Abbey.
The proposed merger is certain to raise fears over job cuts. Halifax employs about 37,000.
John Edmonds, general secretary of the GMB union, said: "We will be monitoring the situation and talking to management to ensure that the workforce is not adversely affected."
The deal may also raise competition concerns because the pair would hold a large slice of the mortgage market.
Lloyds' takeover bid for Abbey is already subject to a Competition Commission investigation. Kitty Andrew, banking analyst at ING Charterhouse, said a deal would be particularly beneficial to the BoS after it missed out on Abbey.
She said: "It's clear the Bank of Scotland needs a deal with someone after its failed merger attempt. Halifax perhaps needs the merger less, although for both it appears quite a reasonable move."
The statement from the banks concluded: "Discussions are continuing and a further announcement will be made when appropriate."
Mark Durling, analyst at Brewin Dolphin stockbrokers, believed the two companies could pose a threat to the traditional domination of Barclays, HSBC, Lloyds TSB and Royal Bank of Scotland.
In particular, a merger may go some way to allaying the fears of the Office of Fair Trading about the Big Four's domination of the small business banking and current account markets. Mr Durling said: "It will add another player to the market, but they would have to go all guns blazing to make an impact."
He said the Bank of Scotland stood to benefit from access to the Halifax's branch network and its associated customer channels, which include the Intelligent Finance Internet banking operation.
The Bank of Scotland, which has its head office at the Mound in Edinburgh, was established by an Act of the Parliament of Scotland on July 17 1695. It is the oldest surviving UK clearing bank.
The merger would be the Halifax's second big corporate move this year after it bought troubled mutual insurer Equitable Life's operating assets in a deal worth a potential £1bn.
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