The Red Devils have spent several weeks trying to convince La Blaugrana to part ways with the midfielder, who burst onto the scene at Ajax under Erik ten Hag.
With De Jong under contract at Camp Nou until 2026, Barcelona have been under little pressure to sell him for a cut-price fee despite his contract situation.
Man United are now understood to have reached a full agreement with Barcelona over a fee for the 25-year-old, who will cost the 20-time English champions an upfront fee of £63m potentially rising to £73m with add-ons.
Barcelona are now pushing to get De Jong out of the door in order to boost their transfer kitty and are supposedly prepared to leave the Netherlands international out of their squad for their pre-season tour of the USA.
However, Sport now claims that De Jong's agent has made it clear to Manchester United CEO Richard Arnold that De Jong has no intention of leaving Barcelona for Old Trafford this summer.
The Red Devils are yet to agree personal terms with the former Ajax protege, and De Jong's stance has supposedly not changed in spite of the fee agreement between the two clubs.
The midfielder and his wife are said to be settled in Catalonia, and he does not want to drop down to the Europa League after helping Barcelona qualify for the Champions League last season.
The report adds that De Jong would not be totally against an exit from Barcelona in the coming weeks, but he is 'flatly refusing' to reunite with Ten Hag at the Theatre of Dreams.
De Jong is said to have been left 'disgusted' by Barcelona's attempts to push him out of the door this summer, but the Dutchman still intends to remain put at his 'dream club'.
Xavi and Ronald Koeman both ensured that De Jong was an integral part of their plans last term, as he hit four goals and five assists in 46 outings for the Blaugrana in all tournaments.
De Jong has totalled 13 goals and 17 assists in 139 games for Barcelona since his £77.4m from Ajax in 2019, but he has only won one Copa del Rey over the past three years.
Barcelona have already added to their midfield ranks this summer with the signing of Franck Kessie, who will compete with Gavi, Pedri and Sergio Busquets for spots in the engine room next term.
Meanwhile, Man United confirmed the signing of Christian Eriksen on a three-year deal on Friday afternoon, with the Danish playmaker following Tyrell Malacia to Old Trafford as the Red Devils' second summer acquisition.
Ten Hag's side - who claimed a 4-1 friendly win over Melbourne Victory on Friday - are also thought to be on the verge of signing Ajax centre-back Lisandro Martinez after Arsenal cooled their interest in the 24-year-old.