Erik ten Hag is keen to reunite with the player he managed last season at Ajax, but Manchester United are yet to meet the asking price set by the Dutch champions.
A recent report suggested that United's failure to close the deal could allow Chelsea to join the race for Antony's signature.
As well as facing competition from Chelsea, the Red Devils could now be rivalled by Liverpool, who are reportedly showing an interest in the Brazilian.
According to the Daily Mail, the Reds have already held talks with Ajax and the player's agent, which could see Liverpool persuade the Dutch club to accept a bid well below the £69m asking price.
The report indicates that the Merseyside club could reach a deal worth £59m, which has brought about a response from Ten Hag who has encouraged United to move quickly for the forward.
Since joining Ajax in 2019, Antony has scored 22 goals in 78 appearances for the club.
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