UPDATE 4-Lufthansa meets Alitalia unions on rescue

(Adds pilots unions signing agreement paragraphs 3-4)

By Alberto Sisto and Deepa Babington

ROME, Sept 26 (Reuters) - German airline Lufthansa (LHAG.DE) met Alitalia's unions on Friday to discuss taking a possible stake in the bankrupt airline as Italy pushed to wrap up labour talks and seal an investor bailout.

Lufthansa and Air France-KLM (AIRF.PA) are jostling for a foothold in the attractive Italian market by making an alliance with Alitalia AZPIa.MI should its proposed relaunch by the CAI consortium of Italian investors succeed.

The investor deal collapsed last week, but lurched back to life on Thursday after winning the support of four major unions, including Italy's largest. After 12 hours of negotiations which dragged into the early hours of Saturday, pilots' representatives also agreed to get on board, the prime minister's office said, clearing a major hurdle towards the deal.

The two remaining flight assistant unions said that there had been "steps forward" and that they would reconvene again for talks on Monday.

Italy's labour minister had hoped to clinch support from the remaining unions by an 1100 GMT deadline, but that passed without having any impact on the talks, which continued. He said CAI, which has now said its offer will expire on Oct. 15, planned to press ahead with its bid, even without their backing.

Prime Minister Silvio Berlusconi, who spent the past couple of days at a health spa due to minor back problems, said he was following "every minute" of the negotiations and urged the unions to turn "from unreasonable into reasonable."

ROMAN MEETING

The four major unions backing the bailout met Lufthansa Chief Executive Wolfgang Mayrhuber on Friday and they said he conveyed the German carrier's interest in Alitalia.

Lufthansa declined to comment specifically on its interest, but said Mayrhuber was in Rome at the Italian government's request to discuss the stricken Italian carrier.

Lufthansa, which has become an active player in European airline consolidation, has long had its eye on the Italian market, but the latest meeting is its clearest demonstration yet of interest in striking an alliance with Alitalia.

"It's evident that (the Germans) are interested just as our interest in them has been obvious," said Raffaele Bonnani, the head of Alitalia's second biggest union, Cisl.

Sources with knowledge of the matter said Lufthansa is mulling whether to take a 20 percent stake in Alitalia that is expected to up for grabs for a foreign investor. A separate union source said the German airline was interested in an even bigger stake.

Rival Air France-KLM, whose deal to buy Alitalia collapsed this year because of union opposition, is also eyeing a stake of as much as 25 percent in the CAI consortium taking over Alitalia, sources familiar with the matter have said.

But it could face an uphill climb with major Alitalia unions openly supporting Lufthansa and signs that Berlusconi would also favour a tie-up with the German carrier after opposing Air France-KLM's deal in the past.