The deal is reported to be worth an initial 80.75 million pounds ($94.74 million), with a further 4.25 million in add-ons, the BBC said.
The 22-year-old is set to complete a medical within the next two days.
Antony joined Ajax in February 2020 from Brazilian Serie A side Sao Paulo, making more than 80 appearances for the Dutch side in all competitions and scoring 25 goals.
He made his Brazil debut in October 2021 in a 3-1 World Cup qualifying win over Venezuela.