Dybala is contracted to the Serie A champions until June 2022 and said in an interview with CNN this week he was waiting for the club to initiate talks.
The Argentina international has struggled for form since Cristiano Ronaldo's arrival at Juve, scoring 23 goals in all competitions since the start of 2018-19, fewer than he managed in 2017-18 alone.
Maurizio Sarri has acknowledged it is difficult for Dybala, who was linked with a move to Manchester United in the previous close season and has expressed an interest in playing for Barcelona, and Ronaldo to "coexist" in the same team.
However, Paratici is optimistic about Dybala's long-term future in Turin.
Ahead of the second leg of their Coppa Italia semi-final against Milan on Friday, Paratici told Rai Sport: "We are not worried, as we started discussing the situation with Dybala and his entourage, so we are absolutely optimistic and confident.
"Everyone who goes to negotiate a contract wants an improvement, so that's entirely logical."
Asked about Juve's reported interest in Roma's Nicolo Zaniolo, he added: "This is not the time to talk about the transfer market, it's already been done when there was no football being played, but we want to fully enjoy this moment when Italian football returns."
Juve's clash with Milan is their first game in over three months, after football was suspended across most of the globe in March due to the coronavirus pandemic.