The Sun reports that United are ready to pay Hysaj’s £44million release clause.
The deal could make the 24-year-old the seventh most expensive defender of all time.
Hysaj has been linked with some of the top clubs in Europe, after enjoying a superb campaign with Napoli.
Jose Mourinho will make signing a new right-back on of his top priorities in the summer transfer window.
Mourinho is also expected to let Italy international Matteo Darmian join Juventus.