In the interview, Gratteri said Francis was moving in the right direction by "breaking down the center of economic power in the Vatican."
"Those who have been nourished by the power and wealth that is directly derived from the church are nervous and agitated," Gratteri was quoted as saying. He said he didn't know if the Mafia could target the pope, "but certainly they're thinking about it. He could be a threat."
The Vatican spokesman, the Rev. Federico Lombardi, said the Holy See was not concerned.
"We are absolutely calm," he told The Associated Press. "Everything is going ahead normally and it seems there's no reason to fuel such alarmism."
Michele Barbero contributed.