Erik ten Hag worked with De Jong at Ajax and is keen to make the Netherlands international his first United signing.
Dutch boss Ten Hag has signed a three-year deal at Old Trafford and knows reinforcements are needed to turn the club’s fortunes around.
But Fabrizio Romano says Barcelona have turned down the offer, while ESPN claim Barca are holding out for an overall package worth €100m (£85m).
The Spanish giants are prepared to offload De Jong to help balance the books amid an ongoing financial crisis at the Nou Camp, but will not let him go on the cheap.
De Jong has reiterated his desire to stay at Barcelona but United are hopeful of convincing the midfielder to link up with his former Ajax boss in Manchester.
‘I can’t say anything about that but I prefer to stay at Barcelona,’ De Jong said earlier in the month.
‘I have already said it before, Barcelona are the club of my dreams since I was little. If other clubs call I will take the call, of course. It is something that is always done.’
Meanwhile, Netherlands hero Rafael van der Vaart has urged his compatriot to join Manchester United this summer.
‘That is of course the most ideal. Then you have a trainer who knows exactly what you can and cannot do,’ Van der Vaart told Ziggo Sport, referring to Ten Hag.
‘United still need a little quality. There are players who can do the same and maybe be better than you or have performed more.
‘As long as those other players are there, he is out of place at Barcelona. At United he could play more like with the Dutch national team. Then he’s the only one of his kind.’