The 22-year-old has impressed since moving to Ajax from Sao Paulo in 2020, since winning nine caps for his country and scoring two goals.
Erik ten Hag, his former boss in Amsterdam, is keen to bring him to Old Trafford and a bid of €45 million (£38.4m) has reportedly been placed.
However, no deal has been agreed as yet and Spurs are hoping to win the race for the Brazilian who scored 12 goals and registered 10 assists in 33 games across all competitions last season.
Ajax want to bring Netherlands international Bergwijn back to the Eredivisie from Tottenham and talks are underway between the two clubs for the former PSV forward.
Tottenham are happy to let Bergwijn go and the Sun report they are keen to make him part of a deal to bring Antony to north London.
Bergwijn has had some memorable moments at Spurs, but has struggled to hold down a regular place in the first team, making 60 Premier League appearances since arriving in January 2019, but only 25 of those being starts.
Discussions will continue between Ajax and both Premier League teams, while Antony will also make his choice between his former boss at Old Trafford and Champions League football under Antonio Conte at Spurs.
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