Fabrizio Romano claims that the Red Devils have reached agreement with the Spanish giants following more talks having been linked with de Jong throughout the off-season.
The 25-year-old, who has been with Barcelona since 2019, made 47 appearances in all competitions last term.
The Athletic reports that the deal is worth 75m euros plus 10m euros in add-ons.
United and de Jong will need to agree personal terms, with new manager Erik ten Hag eager to add another Dutchman to his squad at Old Trafford.
De Jong is understood to prefer to remain with Barcelona but the club’s financial challenges may force his exit.
A delegation of United officials traveled to Barcelona to discuss the deal face to face with the Blaugrana.
The Red Devils have already secured Netherlands left-back Tyrell Malacia from Feyenoord, while ex-Ajax midfielder Christian Eriksen is close to joining.
The squad is currently in Australia for pre-season matches including a clash with A-League club Melbourne Victory on Friday.
Cristiano Ronaldo isn’t part of that pre-season tour, opting out for personal reasons. The Portuguese star had reportedly declined a lucrative approach from a Saudi Arabian club this week.