The wonderkid has managed 12 goals and eight assists across his 39 league outings since leaving Sao Paulo for an initial £13 million during the winter transfer window of 2020.
Antony plays predominantly on the right wing for Ajax, and City's interest could follow the news that Ferran Torres faces up to three months on the sidelines.
Having joined Ajax on an initial five-year deal, he has played a part in their fine Champions League group stage campaign this season with three consecutive victories.
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