United are looking to sign the Brazilian this summer with Erik ten Hag keen on bolstering his attacking options ahead of the new season.
Antony thrived under Ten Hag at Ajax last term with 12 goals and 10 assists in the Eredivisie.
United have already made an approach to Ajax about the 22-year-old but the Dutch champions have made it clear that they want a fee in excess of €70m (£60m) for Antony.
The Times report that Antony is pushing to join United this summer but Ajax are ready to stand firm and have made it clear they want no more high-profile departures after Ryan Gravenberch and Sebastien Haller.
The report claims that United were hopeful that a £40m package would have been enough to tempt Ajax.
Meanwhile, Fabrizio Romano is reporting that the winger’s representatives are now asking Ajax to listen to United’s offers.
Speaking last month, Ten Hag admitted that Ajax would struggle to replace Antony.
‘If Antony were to go, it would be a loss for Ajax,’ Ten Hag said.
‘You have no-one in the current squad who can take over his position. He is top class.’
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