Speculation about a sale produced a big jump in the shares of Italian holding company IMMSI (IMSI.MI), which owns 7 percent of Alitalia. They were more than 16 percent higher by 1200 GMT.

But Air France-KLM, which owns a quarter of Italy's flagship airline, said there were no talks going on.

"There is nothing. There are no negotiations," Air France CEO Alexandre de Juniac told Reuters. He also said that the airline's resources for such operations were extremely limited.

Italian newspaper Il Messaggero had reported on Sunday that Air France was in advanced talks to buy the whole of Alitalia, offering a 20 percent premium to what a group of domestic investors had paid when the airline was rescued in 2008.

Alitalia is currently owned by CAI, a consortium of investors that bought the then-bankrupt airline in 2008.

CAI paid just over 1 billion euros to rescue the airline, weighed down by debt after years of mismanagement, political interference and labour unrest.

The investors in the CAI consortium can exercise options to trade their shares when a lock-up period ends on January 12.

Two sources close to Italian shareholders said there were no formal talks to sell Alitalia, now valued by some analysts at just over 1.1 billion euros. But they also said investors were starting to weigh options ahead of the January 12 lock-up expiry.

"Discussions with the advisors have not yet begun. Investors are starting to think about what to do ahead of January 12," said a source close to one of the investors.

"Alitalia had from the start been talking about the opportunity to look for an industrial partner. Air France is already an investor and if all the pieces fall into place, it (selling to them) would be the easiest option."

POLITICAL HURDLES

Italian investors have approached several banking advisors to help find a buyer.

"It's obvious that there is some movement among investors. The impression is that (Alitalia Chairman Roberto) Colaninno is pushing for a deal with Air France, but not all the shareholders agree," another source close to the situation told Reuters.

Colaninno, who also controls Alitalia shareholder IMMSI, is the head of the CAI consortium.

"Those who took a stake in the rescue deal are not active in the airline sector. They could sell, but they want to make some money," said the first source close to one of the shareholders. "However, the situation is delicate as the elections near."

Mediobanca analyst Massimo Vecchio said in a research note that the only hurdle for a deal was political.

Air France, a long-term partner of Alitalia, tried to take over the Rome-based airline just over four years ago. But the deal was scuppered by then Prime Minister Silvio Berlusconi, who asked the Italian investors to rescue the carrier instead.

Centre-right leader Berlusconi, who is running again for prime minister in a February election, said at the weekend he was still against the airline's sale to a foreign buyer.

Alitalia returned to profit in the third quarter after reporting losses in the first half, booking a net profit of 27 million euros, down from 70 million euros a year before. Net debt rose to 923 million euros at the end of September, up by 61 million euros from the end of June.

CAI is made up of listed and unlisted Italian companies. Amongst the biggest shareholders are Intesa Sanpaolo (ISP.MI), with 8.9 percent, road operator Atlantia (ATL.MI) with 8.9 percent and IMMSI, which also controls scooter-maker Piaggio.

Alitalia, Intesa Sanpaolo, IMMSI and Atlantia declined to comment. (Additional reporting by Lisa Jucca, Massimo Gaia and Andrea Mandala in Milan, Massimiliano Di Giorgio and Stefano Bernabei in Rome, Tim Hepher, Blandine Henault and Cyril Altmeyer in Paris. Writing by Lisa Jucca. Editing by Jane Merriman)

• A Permanent Economic Emergency