The 23-year-old has struggled for the Red Devils this season, failing to register a single goal or an assist in 11 appearances in all competitions.
Man United head coach Erik ten Hag recently admitted that the "noise" surrounding the ex-Ajax forward had hugely impacted his form during the current campaign.
Antony was recently given a leave of absence by his club to deal with allegations of abuse which have been levelled towards him by his ex-girlfriend and at least one other woman.
The situation is ongoing, with police in Manchester and Sao Paulo investigating the claims, and the South American has struggled to make his mark at club level this term.
A recent report claimed that Man United are willing to allow Antony to join Flamengo on loan in January as part of a deal which would see Gabriel Barbosa move in the opposite direction.
However, journalist Jorge Nicola, via his official YouTube channel, has said that he has spoken with Antony's agent, who has insisted that the deal will not occur at the start of 2024.
Meanwhile, transfer expert Fabrizio Romano has also played down suggestions that Antony could be allowed to leave Old Trafford during the January transfer window.
"Many Manchester United fans have been asking me about Antony and if there is some truth in these rumours of a potential loan deal in January to let the player go," he said on his YouTube channel.
"At the moment I am not aware of any negotiations between Man Utd or any other club for Antony in January.
"At the moment, the situation remains very quiet. Man Utd and the player hope to resolve the situation off the pitch as soon as possible because obviously it is going to affect the performances of Antony, this is very human so we can understand that.
"At the same time, they [Man Utd] want to improve the performance as Antony can't continue like this, he knows that very well. He wants to work hard to improve his performances, so the message is very clear.
"At the moment, they are not planning Antony and Man Utd to part ways in January. For now, the situation remains quiet."
Antony arrived at Man United from Ajax in August 2022, with the deal costing the English giants around £86m, and he has scored eight goals and registered three assists in 55 appearances during his time at Old Trafford.