ROME/MILAN (Reuters) - Italian prime minister Enrico Letta said the Venice airport, operated by Save (>> SAVE SpA), must remain in Italian hands following a press report that German airport company Fraport (>> Fraport Frankfurt Airport Srvc Wrldwd AG) was eyeing a stake.

Save, which has a market capitalisation of around $1 billion, runs Venice's Marco Polo airport. It also operates the airport of Treviso, which is about 30 km (19 miles) away from the tourist-packed lagoon city.

"It must remain Italian," Letta said on Thursday after a trilateral meeting with Slovenia and Croatia in Venice, where he said a possible involvement of the Venice airport in the privatisation of airports in Slovenia was discussed.

Earlier on Thursday a source close to the matter confirmed a press report which said Fraport had mandated Mediobanca (>> Mediobanca Group) to explore whether Generali (>> Assicurazioni Generali SpA) and Morgan Stanley (>> Morgan Stanley) would sell their stakes in Save.

The Italian insurer and the U.S. bank jointly with financial services company Finanziaria Internazionale control 40 percent of Save through a shell company.

Generali and Morgan Stanley's indirect stakes in Save amount to around 13 percent and 6 percent, respectively.

A Fraport spokesman said the company would not comment on market speculation.

(Reporting by Massimo Gaia in Milan and Paolo Biondi in Rome, additional reporting by Marilyn Gerlach in Frankfurt)