The striker is one of the most sought-after players in Europe at the moment after scoring 13 goals in Serie A this season.
Arsenal have been linked with a move for the 21-year-old since January, while Juventus are also keeping tabs on the situation.
However, according to Calciomercato, the pair have been overtaken in the race for Dybala by Inter.
The Serie A side have agreed personal terms with the Argentine, who is set for a significant pay rise if he completes a move to the San Siro.
Inter still need to agree a transfer fee with Palermo, who value Dybala at around £30m, but they are hopeful of closing out a deal.
Dybala will be excluded from Palermo's final games to ensure he is not injured ahead of a summer move.
"I've asked [Palermo coach Beppe] Iachini not to play Dybala in these last few games," the club's president Maurizio Zamparini told La Repubblica.
"It's possible that in the next eight to 10 days we'll sell the player, and I want to avoid injuries in this very delicate phase."
