Alfred Schreuder also revealed he doesn't want his to sell any more players this summer despite an 'absurd' offer from United on the table.
Brazilian winger Antony has been a long-term target for new United manager Erik ten Hag, who has had two bids turned down for his former player in Amsterdam.
United have reportedly made offers of €60m [£51m] and €80m [£67m] for the 22-year-old, and reports in the Netherlands claim Ajax are expecting a third bid of €100m [£85m].
The Dutch champions have already sold six crucial first team players during the summer window, including Argentine defender Lisandro Martinez who has already joined Ten Hag in Manchester for £46m.
Schreuder was without Antony for Ajax's 1-0 win against Sparta Rotterdam which kept them top of the Eredivisie on Sunday, after the winger skipped training on Friday and Saturday.
"We have already lost five or six basic players this summer," Schreuder said after the win as quoted by De Telegraaf. "I don't really want to lose another important player.
"It's difficult and I understand such a boy, but you play at Ajax, and more clubs pass by.
"Ajax does play in the Champions League and United do not."
Antony had conducted an interview with De Telegraaf ahead of the match, in which he said he couldn't rule out a move this month.
However, the Dutch outlet also claims that Schreuder is happy to leave Antony out of action until the window closes on September 1, knowing he will need to quickly return in order to secure a spot in Brazil's squad at the World Cup.
The former Club Brugge boss and Ten Hag replacement at Ajax did acknowledge the extraordinary offer though, and also said he'd spoken to the player about it.
"That's an absurd amount of money," Schreuder told ESPN after his team's win.
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"Whether we can also refuse a higher offer, that's not up to me. Then you have to be with the management of the club.
"But I don't want to lose him, and I think Ajax is still reasonably close to cash [financial stability]."
Before the game, Schreuder said of the missing winger: "I spoke to Antony, he has indicated that he does not feel 100 per cent.
"I only want players who are completely with their heads at Ajax. We've talked about it and I think it's a difficult situation, I'm honest about that. I've never been in such a situation myself.
"For myself it is especially important that I have spoken well with him. I have been very clear that I only want players who want to play for Ajax. I think that's the most important thing."