The Red Devils will face huge competition from Barcelona but will be buoyed by the news Dybala has no release clause in his contract.
The 23-year-old was touted as perfect summer replacement after the Catalan giants lost Neymar to Paris St-Germain.
But according to the Daily Mirror, United chief Ed Woodward has told Dybala's representatives if he decides to leave Juventus, Jose Mourinho will be interested in bringing him to England.
Woodward has a good relationship with Juve's general manager Beppe Marotta after the two clubs agreed Paul Pogba's £89m move back in 2016.
Marotta admitted recently the Italian outfit would be powerless to stop Dybala leaving Turin if he wants to move on.
This has put a number of European heavyweights on high alert ahead of the January transfer window.
Dybala gave Barcelona chiefs a glimpse of his talent in their Champions League quarter final meeting back in April, netting twice to knock the Spaniards out of the competition.