The player has been on United's radar since February, with Erik ten Hag's side making two bids this summer alone.
The Dutch champions have lost a large chunk of their squad during the window and were keen to hang on to one of their top stars.
However, the club's efforts to keep the player have only added to his frustrations, which culminated in an explosive interview with transfer guru Fabrizio Romano.
Speaking on his YouTube channel, Romano revealed Antony's comments: "Since February of this year, my agents came to Amsterdam to inform Ajax of my desire to leave the club to face a new challenge and that some interested clubs would arrive and, with them, certainly a great offer.
"During the window months, meetings concluded including a proposal from Ajax for contract renewal. I made it clear once again I want to leave the club.
"Today in a meeting with the board I expressed my interest in leaving the club, this time with a considerable offer on the table. Others have already arrived (but) Ajax always refuses with the argument it only has five days to replace (me).
"I'm not asking (for Ajax) to release me, I am asking Ajax to sell me as the highest bid received by a player who plays in the Eredivisie."
A move to United would see Antony reunited with ex-Ajax boss Erik ten Hag, who has already recruited defender Lisandro Martinez from his former club.
"I was very happy in Amsterdam, I won titles at Ajax, made friends and built part of my career, but now I reinforce that I am ready and full of motivation to follow my story and my dreams," he added.
"People need to listen to me and understand that my motivation moves me towards happiness. I need this to continue performing at a high level. Ajax will always be in my heart."