Ajax manager Alfred Schreuder has revealed that Antony is still recovering from the ankle injury that forced him to miss the final weeks of the 2021-22 campaign.
The 22-year-old scored 12 times and registered 10 assists in 32 appearances for his Dutch club last season, but his campaign ended in March, missing his side's last seven league matches of 2021-22 due to the injury that he picked up while representing Brazil against Bolivia.
Schreuder has admitted that the attacker is not yet ready to return to action, and he could potentially be on the sidelines for the majority of Ajax's pre-season schedule.
"He is still recovering from his injury. But I think the next few weeks are important. For his injury, we hope it improves quickly. I assume that he will be fit at the end of the preparation," Schreuder told ESPN.
Antony's future is currently the subject of much speculation, with Manchester United said to be looking to bring him to Old Trafford during this summer's transfer window.
The South American starred under new Man United boss Erik ten Hag in Amsterdam, and he has allegedly been identified by the English giants as a leading transfer target.
Initial reports had claimed that the Red Devils were looking to do a deal in the region of £40m, but Ajax allegedly value the wide forward at double that price.
"Antony, for instance, is worth £80m in the eyes of Ajax. The prices they are asking for are absolutely huge because they have no need to sell. They know Man United, like many clubs in Europe at this moment, need players. So it's a very awkward position Manchester United are in at the moment," Dutch journalist Marcel der Kraan recently told Sky Sports News.
"Antony, he (Ten Hag) thinks is a great player but he knows he is too expensive at this moment, and that Frenkie de Jong is much more of an important player for him than Antony."
Bayern Munich were also believed to be interested in signing the attacker earlier this summer, but the Bundesliga champions ultimately moved for Liverpool's Sadio Mane.
"It is important to clarify that Man United are focused on Frenkie de Jong and in direct talks with Barcelona, but they are also negotiating for other players. The club is active on multiple deals, including discussions with Ajax on [Jurrien] Timber, Lisandro Martinez (but Arsenal are also working for the Argentine centre-back) and Antony," Italian journalist Fabrizio Romano wrote in his column for CaughtOffside.
Man United have struggled to fill the right side of their attack in recent years, with Jadon Sancho playing his best football off the left for the club in the second half of last season.
The Red Devils are also believed to be keen to sign a new striker this summer but could concentrate their efforts on bringing in Antony, with Cristiano Ronaldo set to again have a key role for the Red Devils next term.
Man United were back in pre-season training on Monday, and Ten Hag is said to be desperate for at least a couple of the club's summer transfer targets to be on the flight for their pre-season tour of Thailand and Australia on July 8.