The 24-year-old has drawn the interest of a number of Europe's top clubs following a string of impressive performances for Juventus, including scoring 15 goals in 21 Serie A appearances so far this season.
United are among the teams consistently linked with Dybala, despite manager Jose Mourinho previously suggesting that he will not be signing any new attacking players this summer.
Italian outlet Rai Sport claims that Dybala is now considering the possibility of leaving Turin at the end of the current campaign due to rising tension between himself and the club.
However, should United go in for the Argentina international then they would likely face stiff opposition from elsewhere, with free-spending Paris Saint-Germain among the clubs also credited with an interest.
PSG have reportedly earmarked Dybala as a possible replacement for Neymar should the Brazilian leave the club for Spanish giants Real Madrid.