The Dutch champions are pushing to land Bergwijn this summer with the player also keen to move on from the Premier League.
With the World Cup around the corner, the Dutchman does not want to remain a bit-part player and wants to join Ajax where he has been promised a big role.
Tottenham rejected a bid from Ajax in January for Bergwijn and another offer was rejected at the end of last season but the Dutch champions are determined to get the deal done this summer.
And according to Dutch daily De Telegraaf, they are prepared to break their own transfer record to take the winger to Amsterdam.
Their current transfer record is held by Sebastien Haller who they signed for €22.5m from West Ham in January last year.
The forward is on the verge of joining Dortmund from Ajax for big money and the Dutch champions are prepared to reinvest the proceeds in Bergwijn.
The fee to take the winger to Ajax is almost certain to eclipse the figure they paid for Haller last year.
However, the negotiations could drag on for some more time and Ajax are keen to do the deal next month.
It would allow the club to record the transfer in the new financial year rather than show the costs of the transfer on this year’s balance sheet.