The French club is keen to lure the midfielder back to his native country and has opened informal talks.
The Ligue 1 champion has long been linked with the France international as the club aims to further strengthen the squad this summer and Al-Khelaifi has now sounded out Agnelli in a bid to test the water over a summer transfer.
Pogba has a contract with Juventus until the summer of 2016 and the Serie A giant is keen to extend the 20-year-old's stay at the club beyond the expiry date of his current deal.
The Italian side is willing to offer the Frenchman a new contract until June 2018, worth 4.5 million euros per year.
However, even though Agnelli stated earlier this week that the powerful midfielder is untouchable, he has previously admitted that Juventus may be unable to hold on to Pogba if a big-money offer comes in and PSG is ready to test the club's resolve.
The former Manchester United man could be offered wages of up to nearly €9 million a season with the Paris giant and Pogba could be tempted to push for a transfer if PSG steps up its interest come the end of the current season.
Pogba will not be available on the cheap, but PSG could include either Ezequiel Lavezzi or Lucas Moura in the deal to soften Juve's demands.
The midfielder has made 34 appearances in all competitions for Juventus this term, scoring eight goals in the process.