That is because Serie A side AC Milan are said to be in advanced talks with the Dutch champions to bring the 21-year-old to Italy.
The youngster has attracted the interest of several big clubs this season having scored nine and assisted eight goals in 17 league games for the league leaders.
Representatives from both United and Liverpool watched Bergwijn back in October and are keen to acquire his services in the January transfer window.
And it had been reported that the Red Devils were set to test PSV’s resolve with a £25m bid for the Dutchman.
It was also believed that Bergwijn was most tempted by a move to Old Trafford but now, according to Italian publication Calciomercato, AC Milan could now step in.
The report suggests that the Rossoneri are already in ‘advanced negotiations’ for the winger, with a January loan deal the most likely option with a view to a permanent deal in the summer.
Bergwijn was recently quoted as saying that he was committed to PSV, regardless of the interest from Europe’s elite.
“I am not concerned with big clubs or with rumours about interest,” he said.
“I have remained with PSV this summer because I want to continue the line here to the end of the season.”
Bergwijn joined the PSV academy from Ajax in 2011 and has progressed into a first-team regular under Mark van Bommel.
He has represented the Netherlands in every age group from Under-17s onwards and has two caps for the senior side.
Bergwijn, a natural wide player, would be an asset for both United and Liverpool and would potentially offer something different for both teams.
Liverpool boss Jurgen Klopp recently suggested that the Premier league leaders would not be bringing in any more faces in January but Bergwijn had become a target.
United interim boss Ole Gunnar Solskjaer is looking for reinforcements to help his bid to get the team into the top four but defensive acquisitions could be the priority.
Bergwijn signed an extended deal in June to stay at the Phillips Stadion until 2022, and PSV rejected bids from Torino and Bordeaux for the player in the summer.
It remains to be seen how far along any AC Milan negotiations for Bergwijn may be.