The Red Devils' interest in the Netherlands international is no secret at this point, as CEO Richard Arnold has revealed that the club are working to get a deal done.
De Jong emerged as one of Europe's top midfield prospects under Erik ten Hag at Ajax, where his development helped him secure a £77.4m move to Barcelona in 2019.
De Jong has remained an integral member of the Blaugrana XI under various managers, and he still has four years left to run on his deal with the Catalan giants.
As a result, Barcelona can afford to play hardball in negotiations with interested parties and have reportedly slapped an €85m (£73m) price tag onto the head of the 25-year-old.
Man United are already believed to have seen their opening bid - which comprised an upfront fee of €60m (£51.5m) and up to €10m (£8.6m) in add-ons - rejected by Xavi's side.
According to Marca, the Red Devils are now preparing to up their initial offer to €75.7m (£65m), but Barcelona are still refusing to budge on their asking price for De Jong.
The report adds that Man United are still hopeful of driving the price down due to Barca's volatile financial situation, but the La Liga giants are feeling more positive about their economic circumstances and therefore feel no pressure to lower their valuation.
Furthermore, De Jong has consistently downplayed links of an exit from Camp Nou, but the ex-Ajax man would supposedly be open to an exit if it became clear that Barcelona were willing to sanction it.
De Jong has scored 13 goals and set up 17 more in 139 games for Barcelona since his 2019 arrival, although he has only won one Copa del Rey with La Blaugrana so far.
The 25-year-old ended the 2021-22 campaign with four goals and five assists to his name from 46 appearances in all competitions, during which he battled emerging stars Pedri and Gavi for spots in the engine room.
Ten Hag will be working without the quartet of Paul Pogba, Nemanja Matic, Jesse Lingard and Juan Mata next season following their exits as free agents, and the former is now on the brink of returning to Juventus.
Despite the plethora of exits - which also includes Lee Grant, Edinson Cavani and soon-to-be Nottingham Forest loanee Dean Henderson - Man United are yet to make one summer signing in the current window.
The Red Devils' lack of early activity led to suggestions that Cristiano Ronaldo had threatened to leave the club, but the five-time Ballon d'Or winner is expected to stay for at least another 12 months.
Man United's midfield ranks will be boosted by the return of James Garner from his loan at Nottingham Forest, and the 21-year-old has outlined his intentions to impress Ten Hag during pre-season.