The Corriere Mercantile newspaper said Perin, considered the heir to Italy goalkeeper Gianluigi Buffon, was found to be over the legal limit during a routine control on Friday.
The report said Perin, 22, argued with police before having his Volkswagen Golf car confiscated. He is expected to be fined and could lose his licence for several months. Genoa FC have yet to comment.
The incident came only days after Perin made his Italy debut in a 1-0 friendly win over Albania, when he replaced Salvatore Sirigu for the last 17 minutes.
Genoa, who have conceded 11 goals in as many games, sit ninth in Italy's Serie A 12 points behind leaders Juventus ahead of Monday's home game against Palermo.