The deal, worth 1.2 billion euros (£874.5 million), was agreed in 2014 but has been thrown into jeopardy following the election of the leftist-led, anti-austerity government in January.

Athens now wants a stake in the consortium, which also includes Greek energy firm Copelouzos, and wants to cut the number of airports in the deal to seven, the source said.

Fraport would be willing to consider a limited amount of state involvement but only if the conditions could be agreed by all sides, the source said, adding that Fraport boss Stefan Schulte had met Greek representatives this week

Fraport said there had been constructive talks with Greek government representatives on the sale but declined to provide details.

A senior Greek economy ministry official confirmed that Greek Economy Minister Yiorgos Stathakis had met the CEO and other board members of the German firm on Wednesday in Athens.

"The meeting took place in a good climate and both sides accepted and agreed that the deal needs to be reviewed," the official told Reuters on condition of anonymity.

He declined to comment on whether Greece had asked for a stake in the consortium or to lease a smaller number of airports.

Fraport has previously said it expects the deal to conclude by the end of 2015 or the beginning of 2016, a slippage from its earlier timetable of the third quarter of 2015.

(Reporting by Peter Maushagen; Additional reporting by Angeliki Koutantou in Athens; Writing by Victoria Bryan; Editing by Andreas Framke and Gareth Jones)