Il Messaggero newspaper said Caio Giulio Cesare Mussolini, a 50-year-old former submariner, aimed to run as a candidate for the Fratelli d'Italia (Brothers of Italy) party.
"So many people want to put Mussolini on the ballot," it quoted him as saying.
Mussolini is the first cousin once removed of Alessandra Mussolini, the dead fascist leader's granddaughter who has been an MEP since 2014.
Born in Argentina, Mussolini has no previous political experience but "obviously I've breathed politics my whole life," he told the daily.
He described himself to Il Fatto Quotidiano as "a post-fascist who refers to those values in a non-ideological way".
He said he thought he was chosen as a candidate not for his family name but for his first names, the Italian form of "Gaius Julius Caesar", as well as his sense of duty and international experience.
If elected, he said he would "defend the national interest with all my actions and votes", in line with the nationalist stance of Fratelli d'Italia.
The party won 4.4 percent of votes in last year's Italian national election.