The passengers travelled to Rome from the Algerian capital, Algiers, and Istanbul in Turkey, Il Messaggero reported on Thursday.
Authorities lost trace of them on landing, as they managed to leave the airport without having their documents checked by security.
The incident happened in September but news of their disappearance only broke on Wednesday, when it was discussed at a meeting between air traffic police and unionists.
The officers have asked for state police chief, Alessandro Pansa, to get involved in the case, Il Messaggero said.
The missing passengers are thought to have avoided getting on shuttle buses, which take new arrivals from the plane to the terminal building. Some may have dressed into clothes similar to those worn by airport ground staff, while others could have jumped the airport fence, the newspaper said.
While the Algerians’ reasons for coming to Italy are unknown, Andrea Margelletti, the president of the Centre for International Studies (CeSi) in Rome, said there were two main theories.
“It’s most easy to imagine that the strange disappearances are linked to human trafficking and illegal immigration or organized crime, perhaps tied to drug smuggling,” he was quoted as saying.