The 22-year-old has allegedly emerged as a leading transfer target for the 20-time English champions, having impressed under new Red Devils boss Erik ten Hag in Amsterdam.
A number of other clubs have also been credited with an interest in the forward, who still has more than three years left to run on his current deal.
However, according to Goal, the Brazil international has made it clear that he wants to move to Old Trafford during this summer's transfer window to reunite with Ten Hag.
The report claims that Man United have held 'informal talks' with Ajax over the attacker but are yet to submit an official offer despite the recent speculation.
Antony is believed to be aware of interest from other leading European clubs but is only interested in leaving Amsterdam to make the move to Manchester.
Ten Hag is said to have mentioned the South American during his first recruitment meeting with Man United, and the club are now ready to back their new head coach.
"I want to thank you for everything you taught me. Know that I will always stand with you if you need me," Antony posted on social media when Ten Hag left to take the Red Devils job.
Last term, the attacker scored 12 goals and registered 10 assists in 32 appearances in all competitions, including eight goals and four assists in 23 Eredivisie outings.
Antony was also in impressive form in the Champions League, scoring twice and providing four assists in seven appearances, as the Dutch giants made the last-16 stage of the competition.
Mason Greenwood also remains suspended by the club, meaning that the Red Devils are short of attacking options at this point of the transfer window.
Ten Hag is believed to want five new signings this summer, including Barcelona's Frenkie de Jong, with talks over a possible deal for the Netherlands international thought to be heading in the right direction.
The 20-time English champions will be back in pre-season training on Monday, although those involved for their countries during the recent international break will not report for duty until next month. body check tags ::