Ajax have reportedly placed an £80m valuation on Antony amid suggestions that Manchester United are keen to sign the Brazil international during this summer's transfer window.
The 22-year-old impressed for his Dutch club during the 2021-22 campaign, scoring 12 goals and registering 10 assists in 32 appearances in all competitions.
New Man United boss Erik ten Hag is believed to be desperate for a reunion with the South American at Old Trafford, with the Red Devils said to be in talks over a potential summer move.
However, according to Dutch journalist Marcel van der Kraan, Ajax value Antony at £80m, which could price the 20-time English champions out of a summer deal.
"Antony, for instance, is worth £80m in the eyes of Ajax. The prices they are asking for are absolutely huge because they have no need to sell. They know Man United, like many clubs in Europe at this moment, need players. So it's a very awkward position Manchester United are in at the moment," Van der Kraan told Sky Sports News.
"We've heard a lot of names but of course Ten Hag has not approached every player in his squad from last season. Yes there was [Jurrien] Timber, but Timber's decided to stay because Louis Van Gaal told him you might be out of the World Cup team if you go to United and you're not playing every week there.
"Antony, he (Ten Hag) thinks is a great player but he knows he is too expensive at this moment, and that Frenkie de Jong is much more of an important player for him than Antony."
The Dutch football expert has also claimed that Lisandro Martinez will be difficult to sign this summer due to his high price amid claims that Man United and Arsenal are both keen on him.
"He (Martinez) is an expensive one because Ajax are demanding £45m-£50m for this player. Ajax have no need to sell anymore players," Van der Kraan added.
Arsenal are thought to be at the head of the queue for Martinez but could ultimately be priced out of a deal for the Argentina international, with Ajax not under any pressure to sell.
Man United are yet to make a signing this summer, but the club are believed to be closing in on the capture of Dutch midfielder Frenkie de Jong from Barcelona.
Ten Hag reportedly has a summer transfer budget of £100m, which could be boosted by player sales, with Anthony Martial and Aaron Wan-Bissaka among those said to be available.
Van der Kraan also said that Harry Maguire and Raphael Varane are likely to be Ten Hag's first-choice centre-backs next season despite their struggles last term.
"Martinez, great defender but he (Ten Hag) can't have two small defenders. He needs one big one and that's why he's sticking with Maguire and Varane. He wants quality, he needs to bring in quality at United," the journalist added.
Man United were back in pre-season training on Monday, although the players involved for their countries earlier this month will not report for duty until July.