Bergwijn, 20, is rated as one of Holland's top young talents and made his debut for his club at 17.
This season the winger has scored two Eredivisie goals in seven games this season, including a dramatic solo goal against Utrecht.
Bergwijn has admitted he holds former PSV star Georginio Wijnaldum as one of his idols, having played with him at the club before the winger signed for Newcastle.
Liverpool ace Wijnaldum returned to PSV earlier this year to watch a game, and made a point of looking out for the young talent, seeking him out in the dressing room after the match.
Bergwijn told AD.nl: "That means a lot to me. Georginio is a player who enjoys a lot of respect and he does well abroad.
"The moment I just came to the A [first team] selection he did a lot for me."
Bergwijn could have joined Wijnaldum at Tottenham
The Dutchman was eventually persuaded to join Liverpool, and has become an important contributor to the team.
Bergwijn is a bright talent who has been compared to both Memphis Depay and Arjen Robben early in his career, and Tottenham would be pulling off a coup if they can get a deal done.
If he is asked to by his club, Wijnaldum might have a shot of persuading him to join Liverpool instead.