The 25-year-old is reportedly close to agreeing a switch to Old Trafford and linking up with his former Ajax manager Erik ten Hag.
There is even speculation that a deal could be wrapped up this week for the talented Barca midfielder.
One man who knows De Jong well is Koeman, having handed him his international debut during his time as Netherlands boss and also managing him at club level with Barcelona.
However, the 59-year-old has raised concerns over a potential transfer to United, implying it’s something the player doesn’t want.
Speaking on Spanish television program Vaques Sagradas, Koeman said: “All I know is that Frenkie wants to stay at Barca. He said that a few days ago.
“But I don’t know if Barca want or need to sell him because they need money. He is one of the few for whom a lot of money can be asked.”
While De Jong did say earlier this summer that he had intention of leaving the Nou Camp, Koeman’s comments could hint that is still the case despite United spending the past few weeks attempting to complete a deal for the Dutchman.
Speaking to ESPN in May, De Jong said: “Of course I hear about the links to Manchester United, but the people in charge of the club [Barcelona] didn’t tell me anything.
“I prefer to stay in Barcelona, I’ve said it before,” he added. “Barca is the club of my dreams since I was little. If other clubs call I’ll take the call, of course; it’s something that’s always done.”