Ajax have left Antony out of their squad for Sunday's Eredivisie clash with Sparta Rotterdam, with Manchester United said to be preparing an improved offer for the Brazilian.
The 22-year-old has been strongly linked with the Red Devils throughout the summer, having starred under now Man United boss Erik ten Hag at Ajax.
Antony has started the 2022-23 campaign in impressive fashion for his Dutch club, scoring twice and providing two assists in three appearances, including one goal and two assists in two league fixtures.
However, the Brazil international did not train with his teammates on Thursday or Friday, with the speculation surrounding his future gathering pace.
Antony has now been left out of the matchday squad for Sunday's game against Sparta Rotterdam, as he allegedly attempts to force a move to Man United.
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According to journalist Mike Verweij, Antony is desperate for Ajax to negotiate with Man United, who could make a new and improved offer at the start of next week.
An €80m (£67.9m) offer is believed to have been turned down by the Dutch champions last week, but according to Goal, Ten Hag's side are lining up a fresh bid.
The report claims that the 20-time English champions are 'ready to close the purchase', with the club's next offer set to be an improvement on the one that was rejected.
Antony, who still has three years left to run on his contract in Amsterdam, scored 12 goals and registered 10 assists in 33 outings in all competitions at club level during the 2021-22 campaign.
The South American recently admitted that he could not guarantee he would remain with the Dutch champions beyond the end of the summer transfer window.
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"No, to be perfectly honest (offer Ajax fans assurances that he would remain at the club), I can't. What I can say is that I want to come to the right decision with my family, business partners and Ajax, which is good for everyone," Antony told De Telegraaf.
"In the end, God determines my future. I am very happy at Ajax, I have a contract until the summer of 2025 and I will give everything for this beautiful club for every second.
"I wear the shirt with pride and from day one I feel at home. If we all decide that I will stay here, then I know that this is the best thing for me and the club.
"It's not like I have to leave. Now I am focusing on playing football and have put all other matters in the hands of my agents and my brother. They will advise me on what is best."
Antony has represented his current side on 82 occasions since arriving from Sao Paulo in July 2020, contributing 24 goals and 22 assists in the process.