Perin is currently spending the season on loan at Pescara.
The 20-year-old's agent, Matteo Roggi, claims the Gunners are keen on the keeper as cover for Wojciech Szczesny.
The agent also claims any club wanting to prise Perin away from Genoa would have to meet his £17.4m price tag.
"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."