United are pushing to sign the winger as new manager Erik ten Hag targets a reunion with one of his standout former Ajax stars.
A deal worth around £40million has been mooted, with Antony reportedly making it clear he wants to explore a possible move to Old Trafford.
New Ajax manager Alfred Schreuder took charge of training for the first time on Friday as pre-season got under way for the Eredivisie champions, but according to widespread reports Antony was missing.
Schreuder has made no secret of his desire to keep Antony, telling ESPN recently: "We want to keep Antony at Ajax. I want to work with him, and the club knows this."
Antony's stance, though, also appears clear as United push to make the first signing of the Ten Hag era.