The Argentine attacker, who can play across the front line, is out of contract this summer with the Italian giants.
Dybala had been heavily linked with a move to Inter Milan, but no deal has materialised.
According to La Repubblica, United and Arsenal are swooping in to offer the 28-year-old another option.
Dybala was linked to United in the past, but no deal ever materialised.
The English clubs are likely to offer him better terms than Inter, but the latter are in the Champions League next season.