The current deal for the Argentina international is set to expire at the end of the season.
Roma's management plans to propose a new, extended contract with the goal of Dybala eventually finishing his career with the team.
The new contract will have more favorable terms than the current one and will be longer than initially expected.
Dybala is currently recovering from a thigh injury and aims to be back in action for Roma's match against Fiorentina following the next international break.