The attacker, who has three years left to run on his current contract, could be heading out the exit door in North London after falling down the pecking order under Antonio Conte.
Although Conte has previously lauded Bergwijn's versatility, the January signing of Dejan Kulusevski has resulted in the Dutchman falling out of favour.
Ajax have been linked with offering Bergwijn a way out of Spurs, but according to ESPN, they will have to meet the asking price set at £21.4m.
The report states that Ajax have had three offers rejected - including two that were made in January - although none of those bids have exceeded €20m (£17.1m).
Bergwijn, who previously played for Ajax's rivals PSV Eindhoven, has scored eight goals across his 83 appearances for Spurs.