On Monday, Antony was dropped from the Brazil squad ahead of CONMEBOL World Cup qualifying games against Bolívia and Peru following fresh claims of domestic violence made against the footballer by former girlfriend Gabriela Cavallin, who has waived her right to anonymity in the UK.
United issued a statement on Wednesday acknowledging the accusations but refused to comment on whether Antony is available to play for the club when approached by ESPN. Antony, 23, denies any wrongdoing.
The statement issued by United on Wednesday read: "Manchester United acknowledges the allegations made against Antony and notes that the police are conducting enquiries.
"Pending further information, the club will be making no further comments.
"As a club we are taking this matter seriously, with consideration of the impact of these allegations and subsequent reporting will have on survivors of abuse."
Allegations were first made against Antony by Cavallin, a DJ and influencer, in June before further claims were made on Monday.
It prompted the Brazil Football Confederation (CBF) to issue a statement later on Monday confirming that the forward had been released from international duty for games during the international break.
The statement issued by the CBF read: "Due to the facts that became public this Monday involving Manchester United player Antony, and which need to be investigated, and in order to safeguard the alleged victim, the player, the Brazilian team and the CBF, the organisation informs that the athlete has been withdrawn from the Brazilian team."
The allegations are under investigation in Brazil and a complaint has also been made to police in the UK after Cavallin made a complaint to police about incidents she alleges occurred in Manchester.
Greater Manchester Police issued a statement Monday that read: "Greater Manchester Police is aware of the allegations made and enquiries remain ongoing to establish the circumstances surrounding this report."
In response, Antony posted a statement on social media on Monday in which he insisted all accusations "are false."
It read: "Out of respect for my fans, friends and family, I feel obligated to speak publicly about the false accusations I have been a victim of. From the beginning I have handled this issue seriously and with respect, providing the due clarifications to the police authority.
"The police inquest is under the cover of justice and therefore I cannot make its content public. However, I can say with confidence that the accusations are false and the evidence already produced and more to be produced show that I am innocent of the accusations made."