Italy's Economy Ministry said potential buyers would have to bid for 30.1 to 49.9 percent of the company, with a stipulation the winning buyer or buyers would then bid for the whole company.
The bidding deadline ends Jan. 29, the ministry said in a statement on its Web site.
Alitalia shares closed Friday on the Milan Stock Exchange at $1.39, up 8 cents, or 6.15 percent.
Alitalia, which has not made an operating profit since 1998, expects to lose more than a quarter-billion dollars this year.
Air France-KLM, Europe's biggest airline, has said it has had talks with Alitalia that could evolve into formal discussions and a takeover. But it said the Italian carrier must first be privately owned, have an improved financial position and agree with the French-Dutch carrier on a business strategy.
The Italian government owns 49.9 percent of Alitalia and has agreed to cede management control.
Meridiana, Italy's third largest airline, also emerged as a potential buyer this week.

