Pogba has a further two years remaining on his current deal with the Serie A champions, but his future has been the subject of much speculation in recent transfer windows.
Both PSG and Chelsea have been among the clubs linked with a move for the 21-year-old, while Arsenal and former club Manchester United have also been reported to be admirers.
However, Marotta is now hopeful of tying up a new deal for Pogba, who has quickly established himself as one of the game’s brightest prospects since joining from from Old Trafford in 2012.
He said: "With Pogba and his agent we started a negotiation and I am optimistic that there may be an agreement soon."
Marotta also says Juventus have tabled an offer for veteran goalkeeper Gianluigi Buffon, 36, to extend his stay, while defender Giorgio Chiellini is close to a new deal.
"The Buffon contract is ready. It is up to him to decide when to come and sign and decide when to stop playing football," he said.
"Chiellini’s contract is in the home stretch."