British challenger bank TSB has received a takeover approach from Banco Sabadell, valuing the business at about $2.6 billion.
It said a deal would accelerate its growth prospects and help it compete with bigger rivals.
Shares in TSB rose sharply today, adding over 23.5% in London trade.
Sabadell, Spain's fifth-biggest bank, has made a proposal of 340 pence in cash for each TSB share, subject to reaching agreement on the terms and conditions of an offer, and talks are continuing.
TSB, Britain's seventh-biggest lender, said it would recommend the offer to shareholders.
The sale would enable Lloyds Banking Group to dispose of its remaining 50% stake of the business.
It was ordered to sell this by European regulators as a condition of its £20 billion government rescue during the financial crisis of 2007-9.
It would also demonstrate the attractiveness of new British banks to foreign investors looking for exposure to Britain's economic recovery through lenders untainted by the misconduct issues which have hampered Britain's biggest banks.
Analysts said counter-bidders could also emerge.
Industry sources have in the past told Reuters Virgin Money could merge with TSB to create a bank big enough to compete with larger rivals. Virgin declined to comment today.
Sabadell is planning to diversify by expanding overseas to offset sluggish growth in its home market, which is in the early stages of recovery following a deep recession.
A number of new banks have emerged since the financial crisis but they have struggled to grow to a size that makes them effective challengers to Britain's 'big 4' banks - Lloyds Banking Group, Royal Bank of Scotland, Barclays and HSBC.
These four banks control over three-quarters of personal accounts and make nine out of ten business loans in the UK.
TSB said it believed Sabadell could support and accelerate its growth in personal banking and help it expand its small business lending.
It currently has only a 4.3% share of the personal current account market in Britain.
TSB listed on the London Stock Exchange in June last year in an initial public offering (IPO) which valued the business at £1.3 billion or 280 pence per share.
