The 20-year-old is widely regarded as one of the brightest up and coming talents in Italy at the moment, and has attracted attention from a host of top European sides.
Barcelona are believed to be monitoring Perin's development, as well as a number of other domestic clubs in Serie 'A', including AC Milan, Juventus, Napoli and Roma, according to the player's representative, Matteo Roggi.
Gunners boss Arsene Wenger is believed to have sent scouts to watch the Italian in action on several occasions this season, as he weighs up a bid to lure Perin to the Emirates Stadium in the summer.
However, his €20million price tag might be a stumbling block for Arsenal, in their search for a new goalkeeper to provide competition for current number one Wojciech Szczesny.
The fact that Perin is under contract with Genoa until 2017 also represents a potential snag to any prospective deal that could take the player to the Premier League, with Roggi already stating that he expects his client to be back at Stadio Luigi Ferraris next season.
"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," he confirmed in an interview with calciomercato.it.
"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."
Arsenal have been linked with a number of different goalkeepers in recent months, including Barcelona's contract rebel Victor Valdes, and long-term Liverpool custodian Pepe Reina.