TSB said it has received a £1.7bn takeover approach from Spanish bank Sabadell.
Shares in Sabadell were suspended after the offer was made on Thursday.
The offer valued the British challenger bank at around £1.7bn ($2.6bn,) with each share being valued at 340 pence in cash, while talks are ongoing.
The approach follows a dramatic period for TSB, which only split from Lloyds Banking Group less than a year ago and rejoined the London stock market as a separate company.
The TSB board said it was willing to recommend Sabadell's offer, adding that the Spanish bank could support its "retail growth strategy".
If a takeover were to go through, Sabadell would "operate TSB as a robust competitor in the UK banking market, building on the TSB brand name," the British bank said.
TSB shares soared more than 25% after the rumours were confirmed on Thursday. Lloyds shares also rose by almost 2% after the news broke. The banking group has a 50% stake in TSB.