Bergwijn has struggled for game-time under new head coach Antonio Conte and it seems he is not keen on using the Dutchman.
He joined Tottenham Hotspur from PSV Eindhoven in January 2020 in a deal worth around £26.7million.
The 24-year-old scored on his Premier League debut with a superb volley in their 2-0 victory over Manchester City and he finished the campaign with three goals in 16 appearances.
In his first full season at the Lilywhites, the Dutchman played an important part in Spurs' impressive start to the 2020/21 Premier League campaign under Jose Mourinho but quickly fell down the pecking order.
A missed chance against Liverpool in December 2020, which cost Spurs at least a share of the spoils saw him dropped by the Portuguese.
He has been unable to work his way back into the team since and could consider a return to a club where he started his youth career.
"Conte doesn't see it in him at all," said the Dutch football reporter, Mike Vermeij.
"Conte is also the one who thwarted Bergwijn's transfer from PSV to Italy. Inter Milan were interested at the time but Conte didn't need him.
"Conte has only said two words to Bergwijn in two weeks at Tottenham Hotspur. That is why Ajax can consider (signing) him."