The 22-year-old has been heavily linked with a reunion with new United boss Erik ten Hag at Old Trafford ahead of the 2022-23 campaign, but the Red Devils are yet to meet the Dutch side's valuation, according to reports.
Ajax are said to value the Brazilian at around €80m (£67.8m) according to a recent report, but with United only offering €60m (£51m), a deal is far from being completed.
Ten Hag has urged the United hierarchy to increase their offers for both Antony and current teammate Lisandro Martinez as a result, but GiveMeSport are suggesting that Chelsea could yet swoop in to sign the winger from under the noses of their fellow Premier League side.
The report reiterates the desire of Chelsea boss Thomas Tuchel to add more firepower to his side next season, following the departure of Romelu Lukaku and the lack of goals from German duo Kai Havertz and Timo Werner in the final third.
Raheem Sterling has been brought in from Manchester City, but moves for Ousmane Dembele and Raphinha have failed to materialise, with the former finally signing a contract extension with Barcelona, and the latter set to complete a move to the Catalan side despite significant interest from Chelsea.
Bayern Munich's Serge Gnabry, as well as Antony, has emerged as a potential alternative for Tuchel, as the German boss looks to close the gap on Man City and Liverpool in the Premier League during the 2022-23 campaign.
Antony enjoyed an impressive 2021-22 campaign in front of goal for Ajax, scoring 12 times and registering 10 assists in 32 appearances across all competitions.