Tuttosport says United have spent the last month trying to convince Dybala about a move to England.
United have been heavily linked with a move for Dybala, who could leave Juventus for a new challenge elsewhere this summer.
Last week, the Argentina international's brother, Gustavo, said: "There are many possibilities that Paulo leaves Juventus. He needs a change."
It is claimed United have been in contact with his family, trying to convince them the player's future is at Old Trafford.