* All offers below firm's market capitalisation - Deoleo
* Deoleo board to study bids in coming days - source
* Buyers to recapitalise Deoleo, not hive it off - source (Adds details on offers and valuation)
By Fiona Ortiz and Andrés González
MADRID, April 3 (Reuters) - A number of foreign funds are vying to take over Spain's Deoleo, the world's top olive oil bottler with brands like Carbonell, a source close to the deal said on Thursday, in a deal that has become highly politicised.
Spain is the world's biggest olive oil producer. Its olive oil exports are surging and the industry is seen as a growth area especially for the south of the country, which is plagued by high unemployment.
With olive-growing rival Italy's state-backed fund Fondo Strategico Italiano (FSI) having expressed an interest in Deoleo, the Spanish government has said it does not want the company to be split up.
The source said six offers were submitted before a deadline on Wednesday, from private equity firms Carlyle and Rhone Capital, both from the United States, Britain's CVC, France's PAI Partners, an Italian fund, and one other.
Rhone Capital, PAI, Carlyle and CVC all declined to comment.
The bids were for a 31 percent stake in Deoleo put on the block by a number of banks that are seeking to shore up capital by selling non-core assets. Italy's FSI on Thursday declined to comment on whether it had put in an offer.
Under Spanish law, a buyer of a stake of more than 30 percent in a listed company must launch an offer for the entire company.
The source close to the deal said advisers would present a recommendation to the Deoleo board in the coming days, and that all of the potential buyers were interested in capitalising the debt-burdened company as opposed to selling off parts of it.
In a statement to the securities regulator on Thursday, Deoleo said the offers it had received - it did not say how many - all valued the company below its market capitalisation, which stands at 486 million euros ($669 million) according to Thursday's closing share price.
Deoleo shares fell 2.38 percent on Thursday to 0.43 euro per share.
"There is very little liquidity in the stock, it's trading at multiples that are completely out of skew with the market," said another source close to the sale, noting the company trades at a premium to other Spanish food companies such as Campofrio , Viscofan and Ebro.
HUGE OLIVE ORCHARDS
While Spain is the world's biggest olive oil producer, it lags Italy in exports outside the European Union, partly because tonnes of Spanish olive oil are sold in bulk to Italy for bottling and re-selling outside the bloc.
Spain has the biggest olive orchards in the world, covering much of the south of the country.
In the past Deoleo - which has 472 million euros of debt, or six times earnings before interest, taxes, depreciation and amortisation (EBITDA) - had rejected an offer from an Italian group to take over its Italian operations and brands.
Deoleo, which controls three of the world's top four olive oil labels - Bertolli, Carapelli and Carbonell - merged last year with a large Spanish cooperative group called Dcoop, which now owns about 10 percent of the company.
A source from Dcoop told Reuters the cooperative wanted to maintain its stake or even increase it rather than accepting a buyout offer, although it has not ruled anything out. "The company has a certain value, we aren't interested at just any price."
However, some companies that had looked at the Deoleo stake have backed away because of the political backdrop, bankers said.
Spanish Agriculture Minister Miguel Arias Canete said on Wednesday that Spain did not want the company to be split up and did not rule out the government taking its own stake in the firm if necessary, although sources close to the deal said that was a remote possibility.
In spite of Canete's insistence that the government does not want Deoleo broken up, he added that the state would not veto any bids.
"The government is following this whole process very closely ... it is maintaining contact with all those involved and with the company's management," he said.
One possible outcome is that Spanish shareholders who do not want to sell could form a consortium with the winning bidder, said one of the sources close to the deal.
Spain is just emerging from a prolonged recession, helped by rebounding exports, and the government has held up the olive oil sector as a key growth driver.
"It's a strategic sector for Spain," Enrique Delgado, secretary general of Infaoliva, an olive oil producers' federation in Spain, told Reuters.
"If another international group moves in, they might be inclined to break up the company. The Italians might want to take back their brands or sell Carbonell, for example."