* Offer values TSB at 340 pence per share
* TSB shares up 24 pct, Sabadell down 6.6 pct
* Analysts say rival bid a possibility
* TSB says it would recommend offer to shareholders
* Sabadell mulls 1.5 bln euro capital hike -source (Adds Sabadell considering 1.5 bln euros capital hike)
By Matt Scuffham and Jesús Aguado
LONDON/MADRID, March 12 (Reuters) - British bank TSB has received a takeover approach from Banco Sabadell, valuing the business at about $2.6 billion and sending its shares soaring by nearly a quarter.
TSB, which set itself up as a challenger to Britain's four biggest banks Lloyds, Royal Bank of Scotland, Barclays and HSBC, said such a move would accelerate its growth prospects and help it compete with rivals.
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.
The Spanish bank is considering a 1.5 billion euro ($1.6 billion) capital hike via a share issue to help finance the deal, a banking source with knowledge of the matter said on Thursday. Sabadell declined to comment.
TSB, Britain's seventh-biggest lender with 631 branches and a 4.3 percent share of the personal current account market, said it would recommend the offer to shareholders. The approach represents a 29 percent premium on Sabadell's closing price of 264.1 pence on Wednesday.
Shares in TSB closed up 23 percent at 327.5 pence. Shares in Sabadell closed down 6.6 percent, their biggest interday fall in 2-and-a-half years as investors contemplated a potential capital hike at the Spanish lender.
The sale would enable Lloyds Banking Group to dispose of its remaining 50 percent stake in the business, which it was ordered to sell by European regulators as a condition of its 20 billion pound ($30 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.
Cross-border takeovers have been rare in the banking sector since the financial crisis, with bigger banks focusing on slimming down to bolster capital and meet tougher regulations.
But industry sources say consolidation could pick up among smaller and medium-sized banks, which are striving to gain the scale required to take on their larger rivals.
Lloyds, which is still 23-percent-owned by the government, said it was "minded to accept" the offer. It would make 850 million pounds from the sale, bringing the total it has raised from selling the business to just under 1.5 billion pounds.
That is nearly double what it would have made if it had gone through with its original plan to sell the business to the Co-operative Bank -- a deal that collapsed when the Co-op's capital shortfall became apparent.
However, Lloyds has spent about 2 billion pounds so far on the entire sale process, sources said. Lloyds must also hand TSB a 450 million pound "dowry" that it had agreed to pay in the event that TSB was taken over.
Lloyds floated the business on the London Stock Exchange last June following the collapse of the Co-op deal. Banking sources said it received informal approaches for the business before it decided on an initial public offering, and for its remaining stake after TSB had listed. But none led to anything firmer until the Sabadell talks.
"There were approaches from various parties but absolutely nothing concrete," said one source with direct knowledge of the matter. The approaches were mainly from private equity parties.
Sabadell started examining the possibility of taking over TSB around two months ago, but formal talks between the two sides only started around a fortnight ago, sources familiar with the matter said. Sabadell notified Lloyds of its interest.
Lloyds was not directly involved in the discussions, the sources said, but it does have an existing relationship with Sabadell, having sold its unprofitable Spanish banking business to Sabadell in April 2013.
That deal saw the Lloyds take a 1.8 percent stake in Sabadell and the two banks form a long-term strategic alliance.
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 on Thursday.
"I suspect that this could trigger rival bids whether it's from Virgin Money or other international players," said Jefferies analyst Joe Dickerson.
Sabadell, which said it would keep the 200-year-old TSB brand, 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.
The deal would be a radical departure for the mid-sized lender, which is based in the Catalan town of the same name in the northeastern Spanish region.
Sabadell, which managed to avoid a state rescue in 2012 at the height of a domestic banking crisis but was still hurt by rotten property loans, has been acquisitive in recent years, though mainly at home. As well as the Lloyds banking business in Spain it snapped up bailed-out lenders.
It has a small presence in the United States and in Mexico, but has started looking for growth overseas in the past year, in search of faster loan growth and as it looks to bulk up profits. ($1 = 0.6668 pounds) ($1 = 0.9422 euros) (Editing by Steve Slater, Giles Elgood and Sophie Walker)