Ajax said they have agreed a transfer fee of 95 million euros (£81 million). Including add-ons, the fee could rise to 100 million euros (£86 million).
Dutch national news agency ANP said that if the deal goes through, it will be a record for an Eredivisie player, surpassing the 86 million euros maximum value of Frenkie de Jong’s move from Ajax to Barcelona three years ago.
Antony has scored 31 goals in 134 club appearances for Ajax and Sao Paulo, and two goals in nine senior appearances for Brazil.
By moving to Old Trafford, the 22-year-old will be reunited with former Ajax manager Erik ten Hag, who has already brought defender Lisandro Martinez to United from the Dutch giants.
“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,” Antony said via Italian journalist Fabrizio Romano on YouTube over the weekend, as he made clear his intention to leave the side.
“During the window months, meetings concluded including a proposal from Ajax for a 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 for the highest bid received for a player who plays in the Eredivisie.”
Antony added: “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…Ajax will always be in my heart.”
The transfer window closes on Thursday evening, when United will be in Leicester seeking a third successive Premier League victory. It is unlikely Antony will be involved against the Foxes, currently bottom of the table.
United started the season with humiliating defeats by Brighton and Brentford only to bounce back with a 2-1 win over bitter rivals Liverpool and last weekend’s tough 1-0 win away to Southampton.
Martinez, Tyrell Malacia, Christian Eriksen and Casemiro have already arrive at Old Trafford during this transfer window.