Juventus director Giuseppe Marotta insisted last week that his side had made no approach for him while also dismissing talk of the Bianconeri making an offer for AC Milan's troubled teenage shot-stopper Gianluigi Donnarumma.
However, the Italian giants are hoping to lure the once-capped Perin to the Juventus Stadium by offering a five-year contract that will see him take home around €2.5m per season.
Perin has already stated he is open to a move this summer, having impressed since making his Genoa debut at the age of 18.
"I'm not afraid to go play in a big club or play the place for a place with another strong goalkeeper," he said recently.
"I've come to a point in my career where I want to test myself and I want to get out of the comfort zone. I can do that now because Genoa helped me to grow and develop. Now I want to get involved and find out how far I can go."
Juve's pursuit of Perin continues after coach Massimiliano Allegri who, after months of speculation surrounding a potential move to Arsenal, has decided to stay in Turin beyond this season after a meeting with the club's board.
Perin is not the first new star expected to head to Juve, either, as they look set to land Emre Can on a free transfer after his contract with Liverpool expires at the end of the season. The Germany international is expected to sign a five-year deal in Italy.