Ajax boss Erik ten Hag is reportedly keen to bring Antony with him to Manchester United this summer.
Ten Hag is the favourite to become the club's new head coach, with the Dutchman recently undergoing an interview with the 20-time English champions.
According to The Telegraph, if the Dutchman is appointed the Premier League team's manager then he will attempt to bring Brazilian attacker Antony with him to Manchester.
The Brazil international has scored 12 times and registered 10 assists in 33 appearances for Ajax this season, including eight goals and four assists in 23 league appearances.
Antony, who largely operates as a right-sided attacker, still has more than three years left to run on his current deal in Amsterdam.
Liverpool and Bayern Munich are also believed to be keen on the South American, who has scored 22 goals and registered 20 assists in 79 appearances for Ajax in all competitions.
Man United also continue to be linked with a move for Chelsea's Antonio Rudiger.
