Ajax have reportedly raised their asking price for Antony to £84m in a bid to ward off interest from Manchester United.
The 22-year-old scored 12 goals and registered 10 assists in 33 appearances in all competitions for Ajax during the 2021-22 campaign, and he is believed to be a leading target for the Red Devils this summer.
Ajax boss Alfred Schreuder recently said that the club were not planning to sell any other important players before the end of the transfer window.
"We have sold a certain amount of players and I am expecting nobody else to leave. We talk on a daily basis. It would be very bad for us if we would lose another starting player," Schreuder told reporters.
Meanwhile, Ajax sporting director Gerry Hamstra later insisted that "nobody is going anywhere now", with the club already selling Lisandro Martinez to Man United.
"I know some of our players are still targeted and they are trying to pull them away," he told reporters. "But we are keeping the squad we have left. Nobody is going anywhere now. We have made it clear to the players, we have had big talks with the players who have a strong desire to leave the club at this moment.
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"Let us make this clear, we did not even want to lose [Lisandro] Martinez, but the figures for the transfer fee were going to such heights that anyone in football knows how it works then.
"We had to let him go. But we still have massive ambitions at Ajax. We play in the Champions League and we can't afford to let go of six key players."
In later comments, Hamstra appeared to soften his stance, claiming that "you can never say never" amid the reported interest from Man United.
"We want to keep this group together. I assume that no-one leaves this core anymore," Hamstra told Voetbal International.
"Of course, you can never say never and I have learned that by now. But we also talk about it with the players and have conversations, also boys who may have a wish to leave. Ajax players are drawn, that is logical."
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However, according to the Daily Mail, Man United have seemingly been priced out of a deal for the Brazil international, with Ajax raising their asking price from £68m to £84m.
Antony and his agent Junior Pedroso are believed to have spoken to the 20-time English champions about a summer move, but Ajax are in a strong position to keep hold of the attacker, having already sold Martinez, Sebastien Haller and Ryan Gravenberch.
The Brazilian has represented his Dutch side on 78 occasions since arriving from Sao Paulo in July 2020, contributing 22 goals and 20 assists.
Man United boss Erik ten Hag is said to be desperate to add at least one attacker to his squad for the new season, but another forward would also be required if Cristiano Ronaldo were to leave the club.
Ronaldo has allegedly not changed his stance despite clear-the-air talks with the Red Devils this week, with the Portugal international still determined to force a move away from Old Trafford.