The Netherlands international continues to be linked with a switch to Old Trafford, with incoming Red Devils head coach Erik ten Hag said to be keen on a reunion with the player that he managed at Ajax.
However, according to the Daily Mail, the 20-time English champions are not prepared to break the bank for the 25-year-old during the summer transfer window.
The report claims that Barcelona want £65m for the Dutchman, who has scored four times and registered five assists in 46 appearances for the Catalan giants this season.
Man United are working with 'a limited budget' due to their failure to qualify for the 2022-23 Champions League, though, so the Red Devils could allegedly be priced out of a move for De Jong.
"We will do what is best for the club. If the economic levers that we want to activate come off, no player will leave for economic reasons," Barcelona president Joan Laporta told Catalunya Radio when questioned on a possible summer exit for De Jong.
"I insist. Let the sports management work. There are players who are quoted to have received offers. In the sports area, Xavi and Mateu Alemany rule and he ends up deciding the club's sports management. I will follow what the professionals of the club say."
Meanwhile, Barcelona boss Xavi also recently conceded that the Dutchman could leave Camp Nou this summer for financial reasons.
"He's an important player for me, and he started every game except for a few due to rotations. But it depends on the economic situation. For me, Frenkie could be one of the club legends," Xavi told reporters.
De Jong has scored 13 goals and registered 17 assists in 139 appearances for Barcelona since making the move from Ajax in 2019.
The midfielder still has more than four years left to run on his contract at Camp Nou and is believed to be keen to stay at the club during this summer's transfer window.
However, Barcelona still have financial problems, and the Dutchman is believed to be viewed as a player capable of raising a big transfer fee in the upcoming market.
De Jong was suspended for Barcelona's La Liga clash with Getafe last weekend but is back in contention for Sunday's match with Villarreal.