Perin's agent, Matteo Roggi, claimed last week the Gunners were among several top European clubs chasing the 20-year-old, who is spending the season at Pescara.
Roggi also revealed Barcelona and AC Milan are keen on the young keeper, while Juventus, Napoli and Roma are other sides to have been linked.
Perin, believed to have a €20million (£17.4m) price tag, is contracted at Genoa until 2017 and his agent has already said he expects the player to be back at the Serie A club for next season.
But Roggi has fuelled speculation linking him with Arsenal by saying representatives from the Premier League club have watched him in action several times this season.
He told calciomercato.it: "We have not had direct contact with any club but I know that Arsenal sent their observers several times to follow him closely and that there are many other clubs interested.
"The certainty is that at the end of this season Mattia will return to Genoa, with whom he recently extended his contract until 2017. And I think that next year Perin will wear the Rossoblu shirt."