Parisi is of a mind that the Italian champions have agreed a deal with the Dutch forward "for some time" despite his contract with Arsenal not due to expire until next summer.
Juventus, Manchester United and Manchester City have been heavily linked with a move for the 28-year-old Euro 2012 forward.
Amid reports that Juventus will try to sign City forward Edin Dzeko if they fail to land Van Persie, Parisi had this to say to an Italian television station.
“I think Juventus have had a signed contract with Van Persie for some time locked away in a notary’s desk.
“It is just my opinion, but I think there’s an eight out of 10 chance the Dutchman will join the Bianconeri.
“Juventus want to win and he is considered the ideal addition to achieve that. I don’t think Edin Dzeko is the right player for the Bianconeri.”