Dybala scored 23 goals in his first season for the Serie A champions and is attracting interest from Real Madrid, Barcelona and Manchester United.
Juventus are therefore looking to extend the Argentinian's stay in Turin in order to prevent other teams making a move.
It is reported that Juve want to double Dybala's contract from €2.2m to €4.4m and extend his stay at the Juventus Stadium until 2021.