Antony has publicly expressed his desire to leave Ajax after the Eredivise club rejected a €90m (£76m) bid from Manchester United.
The 22-year-old winger is United's priority transfer target during the final week of the window but the Old Trafford club's latest bid was rejected on Friday.
United had already seen a bid of €80m (£68m) rejected last week, with Ajax holding out for closer to their €100m asking price due to a lack of time to find a replacement.
It remains to be seen whether United increase their offer for the Brazil international. Cody Gakpo, the PSV Eindhoven winger, has been considered as an alternative if a deal for Antony is not considered possible, while United retain an interest in Chelsea’s Christian Pulisic.
Antony is nevertheless eager to reunite with his former manager Erik ten Hag and went public with his desire to move to Old Trafford in an interview with journalist Fabrizio Romano on Friday night.
"In June of this year, I interrupted my vacation and came personally to inform the managers of Ajax, including new coach, about my wish to leave and that they should consider this possibility, because it was a project for two seasons," he said.
"During the window months, meetings continued and I also received a proposal from Ajax for contract renewal. I made it clear once again: I want to leave.
Antony added: "Today, in a meeting with the club, I expressed my old interest in leaving, only this time with a considerable offer on the table. Others had already arrived. Ajax refused with argument that they only have five days to replace me.
"I'm not asking Ajax to release me, I'm asking Ajax to sell me with the highest bid ever for Eredivisie player. I've been insisting on this theme since February so that the club could rebuild the team with peace of mind.
"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.
"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.
"I hope Ajax fans understand me because the future for a football player is a totally uncertain thing and the opportunities can be unique. My message to them is one of gratitude for Ajax, club and fans."
Ten Hag admitted on Friday that United are still in the market for new arrivals this summer, despite already adding left-back Tyrell Malacia, centre-half Lisandro Martinez and midfielders Christian Eriksen and Casemiro.
“We need players, clear, but we need the right players,” the United manager said. “The whole transfer window, we are happy with what we did until now but the bar has to be high.”
