The government's seven-month auction to privatize the ailing carrier collapsed last week when Air One, the last credible bidder, pulled out saying the terms did not give it enough freedom in restructuring the airline.
Air One, Italy's second-most traveled carrier, said its chairman, Carlo Toto, confirmed the continued interest in Alitalia during a meeting with the speaker of the lower chamber of Italy's parliament, Fausto Bertinotti.
Shares in the airline were up 2.7 percent to EUR0.79 (US$1.09).
In the wake of the failed auction, Finance Minister Tommaso Padoa-Schioppa was expected to discuss the government's plans for Alitalia during an appearance at a parliament committee meeting later Thursday. Among the options are direct talks with interested parties or another auction with different terms.
Beset by frequent strikes, management shuffles and an aging fleet and hurt by aggressive competition from low-cost carriers, Alitalia loses between EUR1 million and EUR2 million (US$1.4 million and US$2.8 million) a day.