The 25-year-old has been involved in a protracted transfer saga surrounding a potential move to Old Trafford, where he would link up with former Ajax boss Ten Hag.
Barcelona initially resisted Man United's attempts to prise De Jong away from Camp Nou, with Joan Laporta insisting that the Netherlands international was not for sale.
However, the Red Devils are now understood to have agreed a £72m deal to bring De Jong to the Premier League, but convincing the midfielder to make the move has been challenging.
De Jong has referred to Barcelona as his "dream club" and was previously understood to have had no intention of heading for the Camp Nou exit door amid interest from the Red Devils.
Now, The Mirror claims that De Jong's public stance differs from his private feelings, and the Dutchman is in fact open to a switch to the Red Devils this summer.
De Jong is supposedly owed as much as £17m by Barcelona in deferred wages, and the midfielder and his agent Ali Dursun are therefore employing a specific strategy to obtain the full payment.
The report adds that the duo do not wish to go public with De Jong's intention to join Man United, as this may weaken their position in negotiations with Barcelona over the unpaid monies.
Man United are believed to have offered to pay De Jong's deferred wages, but the 20-time English champions are unable to do so due to UEFA and FIFA guidelines.
However, De Jong and Ten Hag are said to be in constant dialogue, and the latter is willing to wait until the last knockings of the window to seal a deal for his ex-Ajax protege, who was named in Barcelona's squad for their pre-season tour of the United States.
De Jong - who is believed to earn in the region of £320,000 per week at Camp Nou - has amassed 13 goals and 17 assists in 140 outings for Barcelona in all tournaments since 2019.
La Blaugrana have made two big-money signings in the shape of Raphinha and Robert Lewandowski this summer, as well as agreeing contracts with Ousmane Dembele, Andreas Christensen and Franck Kessie.
As a result, the cash-strapped Catalans are determined to balance the books by offloading De Jong and have been pushing for the midfielder to accept the offer on the table from Man United.
The Red Devils have already bolstered their midfield with the acquisition of Christian Eriksen on a free transfer, with the Dane following Tyrell Malacia to the club this summer.
Lisandro Martinez is also on the verge of sealing a £46.8m switch from Ajax after confirming his imminent arrival in Manchester last week.