Reuters quoted a banking source familiar with the matter as saying that in order to help finance the deal, Banco de Sabadell is considering raising capital of €1.5bn ($1.6bn) through a share issue.
Sabadell is proposing to offer 340 pence in cash for each TSB share. BBC reported the lender has untill 9 April to make an offer.
TSB said any offer by Sabadell will be subject to the completion of due diligence.
Lloyds Banking Group also said in a statement that it "would be minded to accept an offer at this [340p] price if it is made".
During the UK financial crisis of 2007 to 2009, Lloyds had been ordered by European regulators to sell TSB as a condition of its government bailout. The company was given time until the end of 2015 to sell the rest of its stake in TSB.
Acquisition by Sabadell will help TSB to support and accelerate its retail growth strategy, while expanding its presence in the small and medium-sized enterprises (SME) sector.
The Spanish firm plans to continue to operate TSB as a competitor in the UK banking market, building on its brand name.
TSB said that Sabadell expects to finance the transaction on a capital neutral basis for the Sabadell group.The transaction is expected to be neutral to Sabadell earnings in the short term.
Image: Headquarters of Banc Sabadell in Sant Cugat del Vallès. Photo: courtesy of Banc Sabadell/Roso Ribas
