(Corrects quote from Lufthansa's Franz, to show it is Alitalia, not Lufthansa that would welcome Etihad's investment)
* CEO says Alitalia partnership very important
* Alitalia in exploratory talks with Etihad
* Air France-KLM cost-cutting plan on track
By Natalie Huet
PARIS, Jan 23 Air France-KLM will look at reinvesting in Italian carrier Alitalia if the conditions it set for its restructuring are met, the Franco-Dutch airline's chief executive said on Thursday.
Alitalia, which was privatised in 2008, has been unprofitable for more than a decade and has been stuck in a months-long tussle with Air France-KLM over whether to keep their strategic and financial partnership alive.
The Italian airline is in exploratory talks on a possible investment by Abu Dhabi-based carrier Etihad Airways, which sources say is willing to buy a stake of up to 40 percent, to help keep it flying.
Alitalia needs money to invest in more lucrative long-haul routes after a focus on domestic and regional flights left it vulnerable to competition from budget carriers and high-speed trains.
Air France-KLM, which owns around 7 percent of Alitalia, wants the airline to restructure its more than 800 million euro ($1.1 billion) debt, cut costs more aggressively and be willing to come under the Franco-Dutch group's full control.
"These three conditions have not been fulfilled so far, but they're still on the table," Air France-KLM Chief Executive Alexandre de Juniac told reporters on Thursday.
Air France-KLM wrote off the value of its investment in Alitalia and snubbed the airline's emergency fund-raising in December, allowing its stake to fall from 25 percent.
Juniac said he would not get involved in the Etihad talks and was confident that Etihad would not make any hostile move that could jeopardise Air France-KLM and Alitalia's partnerships, notably in maintenance and cargo.
"Our partnership with Alitalia is very important," Juniac said.
The chief executive of rival German airline Lufthansa said he could imagine that Alitalia would welcome investment from Etihad.
"Alitalia needs money and nobody else is around," Christoph Franz said at the annual World Economic Forum in Davos, Switzerland.
Air France-KLM, which is in the middle of its own restructuring as it seeks to attract higher-paying customers and boost its presence in emerging markets, also said its three-year cost-cutting plan was starting to bear fruit.
"The company is doing better. There is still a lot of work to do, we're clearly not completely out of the woods, but we're starting to see the light," Juniac said. ($1 = 0.7372 euros) (Additional reporting by Ben Hirschler in Davos; Writing by Victoria Bryan and Natalie Huet; Editing by Erica Billingham)