The 22-year-old winger has more than three years left on his Ajax contract but he is expected to move on in the summer amid big demand for his services.
Liverpool are amongst the Premier League clubs who have an interest in him and even Manchester United and Manchester City are believed to be keen to get their hands on the Brazilian.
Antony also has suitors in Italy where Juventus have identified him as a potential replacement for Paulo Dybala.
And according to Italian daily Tuttosport, Ajax have identified a big asking price given the interest the winger has been attracting.
Ajax are aware that they could lose Antony in the summer, but are prepared to dig in their heels to get top money for him.
The Dutch champions want around €60m to €70m before agreeing to sell the winger in the coming months.
Ajax believe that given the calibre of clubs interested in Antony, they will be able to get the money they want from his departure.