"We are Italy's flag carrier, so we hope the new government will recognise that and work with us, because we want to grow," he said at a news conference in Rome, describing ITA, the successor to Alitalia, as a "huge political problem".
ITA is fully owned by the state, but a consortium led by US private equity fund Certares has been in exclusive talks since August with the Italian government over taking a 50% plus one share of the airline.
Takeover talks are meant to conclude by 31 October.
Certares, backed by Air France-KLM and Delta Air Lines, is willing to pay €350 million, two sources close to the matters told Reuters last month.
According to its own presentation, Ryanair currently has a 40% share of the Italian airline market, versus 11% for EasyJet and 10% for Wizzair, two other low-cost carriers, and 9% for ITA.
Ryanair is Europe's biggest airline, and O'Leary said he expected its share of the Italian market to grow to "over 50% in the next three years", thanks to an overall increase in traffic and by winning business from rivals.
On Tuesday 18 October, Ryanair said it would add 18 routes to and from Italy in its winter schedule, taking the total to 70, and would invest $1.3 billion in Rome's two airports, the main one at Fiumicino and the one used mainly by low-cost airlines at Ciampino.
O'Leary said he was keen to meet with Italy's new government - due to be installed by the end of the month following the 25 September win by a right-wing bloc - to discuss an agenda of lower taxes and fewer restrictions.
"Real Growth" Sector
"We think tourism will be one of the real growth sectors in Italy for the next three or four years, if the government does sensible things like scrapping the municipal (airport) tax and lifting restrictions on Ciampino," he said.