The Brazilian is cooperating with police investigations into allegations of domestic violence.
Antony landed in the UK earlier this week from his home, where he did not face any charges following an investigation by Brazilian police.
A Manchester United statement issued this morning read: "Since the allegations were first made in June, Antony has cooperated with police investigations in Brazil and England and continues to do so.
"As Antony's employer, Manchester United have decided that he will resume training at Carrington, and will be available for selection, while the police investigation continues. This will be kept under review pending further developments in the case.
"As a club, we condemn acts of abuse and violence.
We recognize the
importance of protecting all those involved in this situation, and we
acknowledge the impact these allegations have on victims of abuse."
The Red Devils were beaten by Brighton & Hove Albion and Bayern Munich after the international break but have recorded back-to-back wins for the first time this season with victories over Burnley and Crystal Palace.
After knocking
them out of the Carabao Cup on Tuesday, Man Utd welcome Palace back to Old
Trafford in the Premier League on Saturday.