United, Liverpool, Bayern Munich and even Inter Milan have their eye on the Dutch international after a superb season in the Eredivisie.
Bergwijn is under contract until 2022 and PSV will be hoping that a bidding war takes place in the summer in order to receive top dollar for their prized asset.
Manchester United have been the favourites to sign the forward in recent weeks.
However, the Sunday Express suggest Liverpool have now joined the race, along with Bayern Munich.
Although, Manchester United have already sent scouts to watch Bergwijn.
The Red Devils opted to send representatives to watch the 21-year-old at FC Emmen last Sunday.
And Bergwijn provided his ninth assist of the season as PSV came away from a tough fixture with a 2-2 draw.
The pacey hitman has already scored 10 goals during the campaign.
The Express claim United wanted to watch Bergwijn perform out of his comfort zone at Emmen’s compact 8,000-capacity De Oude Meerdijk stadium.
PSV led the game 2-0 before being pegged back by two goals in the last 10 minutes.
Bayern also had a scout in attendance and are searching for young blood to boost their ageing squad as they look to rebuild.
Earlier this season, the forward said: “I am not concerned with big clubs or with rumours about interest.
“I have remained with PSV this summer because I want to continue the line here to the end of the season.”
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.