The Brazilian winger is the key attacking target for United boss Erik ten Hag this summer.
The Dutchman wants to reunite with Antony, who he coached to a high level at Ajax over the past couple of seasons.
Ajax technical manager Gerry Hamstra admits the club wants to keep Antony, but he cannot promise the fans the winger will stay.
He told Voetbal International: "We want to keep this group together. I assume that no one leaves this core anymore.
"Of course you can never say never, I have learned that by now.
"But we also talk about it with the players, have conversations. Also with boys who may have a wish to leave.
"Ajax players are drawn, that is logical."