The Red Devils have not made any signings so far this month.
But that could change as The Sun reported that Bergwijn was interested in a move to Old Trafford.
The Dutchman has scored 10 goals this season and assisted nine times in all competitions this season.
And footage has emerged of what the 21-year-old can do.
In highlights from the league, the forward shows off his ability to move past defenders with ease.
He can also put the ball into the danger area, setting up his PSV team-mates whose goals have put them top of the Eredivisie.
In one clip, Bergwijn receives the ball in the middle of the park.
The Dutchman has an opponent running towards him – but a quick flick removes him from the game.
He skips past another defender and is one-on-one with the keeper.
Bergwijn tries to set up his team-mate but it does not quite come off.
The 21-year-old also showed he can find the back of the net too, striking from distance with accuracy.
Since being posted on Monday, this footage has been viewed over 40,000 times.
“This is a Man United player 100%”
Man Utd fan
And the Untied faithful expressed their excitement at the rumours.
“This is a Man United player 100%,” one supporter said.
Another commented; “Welcome to United.”
While a third compared him to a Liverpool forward.
“Hope United sign him before someone else does,” they said.
“He plays like Sadio Mane.”
And a fourth added: “He’ll be the next Mane.”
But fans were also left concerned about Alexis Sanchez after what he did at the Unicef Gala Dinner.