Lufthansa declined to comment on Rome's decision to offer an initial minority stake.
Some of Italy's politicians consider ITA as the heir to cultural icon Alitalia, which they want to preserve.
Some also say that ITA does not have to worry so much about losing its national identity should Lufthansa take over.
The Certares-led alliance was willing to pay 350 million euros for a 50% stake plus one share of the state-controlled airline, sources had said.
($1 = 0.9412 euros)Reporting by Angelo Amante in Rome and Joanna Plucinska in London; additional reporting by Giuseppe Fonte in Rome.