TSB’s board of directors have indicated that they are happy at the proposed price of 340p per share after holding talks with Sabadell.
In a statement, the UK’s seventh largest lender said reaching an agreement depends on “other terms and conditions of any offer".
Lloyds Banking Group currently holds a 50% stake in TSB, but the group is required to sell the rest of its shares by the end of the year as a condition for being bailed out by the UK taxpayer during the financial crisis.
TSB's statement said: “Based on preliminary discussions, the board of TSB believes that Sabadell could support and accelerate TSB’s retail growth strategy and accelerate the expansion of TSB’s presence in the SME sector.
“Sabadell recognises the achievement of TSB’s management and employees and would continue to operate TSB as a robust competitor in the UK banking market, building on the TSB brand name.”
Shares in TSB have soared by more than 25% to 331p since the offer became public knowledge.