Banco Sabadell, which is currently seeking to defend itself from being taken over by a major rival, said it will weigh up any potential offers for TSB.
In a regulatory filing, the banking giant said it received “preliminary non-binding expressions of interest for the acquisition of the entire share capital of TSB.”
TSB currently runs around 175 branches across the UK.
It comes a decade after Sabadell bought TSB for £1.7 billion to gain a foothold in the UK, a year after Lloyds had spun off TSB in a stock market float.
Last month, TSB saw first-quarter profits nearly double thanks to cost-cutting and improved mortgage lending ahead of April’s stamp duty deadline.
The lender posted pre-tax profits of £101.3 million for the first quarter, up from £53.4 million a year ago.
The Financial Times reported that potential bidders for TSB could include Barclays, NatWest, Santander UK and HSBC.
The potential disposal comes as Sabadell seeks to rebuff a potential hostile takeover by Spanish rival BBVA.
BBVA has launched an 11 billion euro (£9.4 billion) move to take control of Sabadell and plans to put this offer in front of shareholders in the coming months.
The potential sale of TSB is the latest in a flurry of recent dealmaking moves in the UK banking sector.
On Monday, Metro Bank shares jumped after reports it had attracted a takeover approach from investment firm Pollen Street Capital.
Meanwhile, Santander has reported pushed back bids from NatWest and Barclays to buy its UK retail bank.