The 27-year-old's future with the Serie A giants is in doubt as they are yet to negotiate a new deal with the player, who will see his contract expire at the end of next season.
According to Tuttosport, Chelsea and United are both monitoring Dybala's situation and are prepared to make a move for him this summer if they are made aware of his availability.
However, Ligue 1 outfit PSG are believed to be the frontrunners for the Argentine's signature, who may be persuaded to join up with compatriot Mauricio Pochettino as well as star attackers Neymar and Kylian Mbappe.
After announcing losses of £99m since the turn of the year, Juventus are prepared to sell up to six first-team players this summer and may be forced to cash in on one of their star names such as Dybala or even Cristiano Ronaldo.
Dybala has suffered with injuries throughout this campaign and as a result has featured just 18 times in all competitions, scoring four goals and providing two assists.