Divers began the search for Russel Rebello, whose body was not found after the ship capsized in January 2012, killing 32 people, on Tuesday morning.
A skull was found on the ship's third deck later in the day, La Repubblica reported.
Genoa Prosecutor Federico Manotti has ordered a DNA test on the remains to establish whether they are that of Rebello or Maria Grazia Tricarichi, whose decapitated body was recovered from the wreck in October 2013.
The result of the DNA test is expected within the next few days, the police said in a statement.
"Both the families of Russel Rebello and Maria Grazia Tricarichi have been informed because we can't rule out the possibility that the remains are hers," the statement added.
"Any information will be communicated as soon as it is available."