Perin is spending the season on loan at Pescara, who were promoted to Serie A last term, and has made the No.1 spot his own, with his performances thought to have drawn the attention of several European heavyweights
The 20-year-old's agent, Matteo Roggi, claims the Gunners are keen on the keeper amid speculation they could bring in cover for Wojciech Szczesny in the summer.
Roggi has also claimed interest from the likes of Barcelona and AC Milan but says the youngster will spend at least next season at Genoa after agreeing a new deal to keep him there until 2017.
The agent also claims any club wanting to prise Perin away from Genoa would have to meet his €20million (£17.4m) price tag.
Roggi told tuttomercatoweb.com of the keeper, capped once for Italy: "There are many clubs interested in him: Arsenal, Barcelona, AC Milan. It has also been said about Juventus, Napoli and Roma.
"Currently, however, there is only one certainty about Mattia's future: he will return to Genoa at the end of his loan and there is a mutual intention for him to spend at least one season in a Genoa shirt.
"Just a month ago we extended his contract until 2017 and Mattia's cost is at least €20 million.
"I am 99 per cent sure he will be Genoa's goalkeeper next season."