The Red Devils have been linked with the Netherlands international since the end of May, with Erik ten Hag believed to have identified the midfielder as his leading transfer target in early meetings with his new club.
Man United are believed to have come to an agreement with Barcelona over a €85m (£71.5m) deal, although a number of issues are currently preventing the move from going through.
There is also a huge problem surrounding the deferred wages that De Jong is owed by Barcelona, with the club thought to be refusing to pay the £17m that the midfielder is demanding.
A recent report claimed that Man United have agreed to pay the £17m, with the fee potentially being paid through bonuses and wages, as it would be illegal to assume the debt.
Due to Barcelona's ongoing financial issues and the problems caused by the COVID-19 outbreak, De Jong came to an agreement which would see him have the money transferred over the remainder of his deal, which is due to expire in 2026.
According to the Manchester Evening News, the 20-time English champions are becoming frustrated with the situation, with the saga seemingly having no clear end point.
The report claims that Man United are 'reluctant to walk away' but could be forced to assess the situation if the end of the window draws closer with a deal seemingly not in sight.
Barcelona president Joan Laporta recently insisted that the club are keen to keep hold of the midfielder this summer.
"Frenkie is Barca player. We want him to stay, he wants to stay. We've received important bids for him but he's our player," Laporta told reporters. "You know salary budget situation; so we will do our best to keep Frenkie at Barca... and I hope he'll do the same."
De Jong made 46 appearances for Barcelona in all competitions during the 2021-22 campaign, contributing four goals and five assists in the process, but his huge wages and ability to raise a high transfer fee are said to be the main reasons why Xavi's side are keen to sell him.
During Friday's press conference ahead of the clash with Brighton & Hove Albion on Sunday, Man United boss Ten Hag insisted that the club would only sign "the right players" before the end of the window.
"The current squad, they make good progress. I'm happy with the signings until now. We just don't need any player, you need the right players and that's the point where we're working all together," said the Dutchman.