It's claimed that United are prepared to go above the £51m offer they made to the Dutch side.
However, their next bid is unlikely to meet Ajax's demands of £68m which means that the deal is far from certain to take place.
Erik ten Hag is keen to have Antony in his team after working with him in Amsterdam. Previously, United have already signed Lisandro Martinez from the same side.
That deal, however, means that Ajax are under no financial pressure to sell the Brazilian which makes the negotiating process frustrating for the Red Devils.
Source: Goal
