The Brazilian right-winger was a key target for manager Erik ten Hag.
However, the Red Devils have been put off by the outlandish price Ajax have set on the attacker.
The Dutch club are loathe to lose their prime attacking talent with the 2022-2023 season underway.
According to Dutch media outlet De Telegraaf, any move for the 22-year-old is dead for this transfer window.
United may try again for Antony in a year, presuming ten Hag is still in charge at the Old Trafford club.
The Red Devils have began the Premier League season with two defeats from their first two games.