The 22-year-old emerged as one of Erik ten Hag's key attackers during the 2021-22 season and has been tipped to reunite with the Dutchman at Old Trafford.
Alfred Schreuder has taken over at Ajax following Ten Hag's Manchester switch, and the 49-year-old has affirmed that he is keen to retain Antony's services.
"We want to keep Antony at Ajax. He has a contract until 2025. I want to work with him, and the club knows this," Schreuder told ESPN when questioned on the Brazilian's future.
However, fuel was added to the fire surrounding Antony's future when the former Sao Paulo youngster did not report for pre-season training on Friday.
The reason for Antony's absence is currently unknown, but the South American's agents are supposedly pushing for the attacker to make the switch to Man United this summer.
Antony was signed by Ten Hag's Ajax for a £14.2m fee in the summer of 2020, and the Brazil international has scored 22 goals and set up 20 more in 78 outings for the Amsterdam giants over the past two seasons.
Antony hit double figures in goals and assists in all competitions during the 2021-22 season, scoring 12 goals and providing 10 assists in 32 appearances as Ajax won the Eredivisie title.
The former Sao Paulo youngster is not the only Ajax player tipped to follow Ten Hag to Old Trafford, but the Red Devils will seemingly be forced to concede defeat in their pursuit of defender Jurrien Timber.
Netherlands manager Louis van Gaal previously warned Timber against a move to Man United, and Schreuder also expects the 21-year-old to stay put in his homeland.
"I have spoken with Jurrien and I am assuming he is staying at Ajax. Timber is a smart guy and he knows what is best for himself. We think he is not done at Ajax yet," Schreuder told ESPN.
Fellow centre-back Lisandro Martinez has supposedly emerged as an alternative target, but Arsenal are thought to be ahead of Man United in the race for the Argentine.
Despite seeing Edinson Cavani, Lee Grant, Paul Pogba, Jesse Lingard, Juan Mata and Nemanja Matic all leave the club this summer, Man United are yet to make a new signing in the current window.
The 20-time English champions remain locked in talks with Barcelona over a move for Frenkie de Jong but are reportedly still falling short of the Catalans' asking price.