An initial fee of 75million euros (£63.5m) rising to a potential 85million euros (£72m) is believed to have been agreed with Barca, but there remains some way to go in the deal.
De Jong is understood to be owed a substantial amount in deferred wages by cash-strapped Barcelona and the Dutchman will need convincing to leave the LaLiga giants.
But United would surely not have pursued the 25-year-old all summer if they did not believe he was willing to move to Old Trafford, where he would work under his former Ajax boss Ten Hag.
United are in advanced talks to sign the Argentina defender from Ajax, with a fee reported to have been agreed to sign a player that is keen on moving to Old Trafford.
The executive pair remained in Europe as United jetted off on their pre-season tour of Thailand and Australia. Ten Hag’s men face Melbourne Victory at the MCG on Friday having beaten Liverpool 4-0 in Bangkok on Tuesday.