Antony and his agent watched Manchester United play Liverpool at Old Trafford on Monday night.
United unveiled the signing of Casemiro from Real Madrid before kick-off, but the Manchester Evening News understands Erik ten Hag is still keen to strengthen his attacking options this summer, with Ajax winger Antony firmly on the club's radar.
Antony contributed 12 goals and 10 assists in 32 appearances for Ajax last season, which was an improvement on his already impressive debut campaign after signing from Sao Paulo, and Ten Hag would like to work with the player again.