The Brazil international, who strongly denies the accusations, was given a leave of absence by United on September 10.
He returned to England earlier this week and attended a voluntary interview with Greater Manchester Police on Thursday.
United have confirmed the 23-year-old will rejoin training with a view to returning to Erik ten Hag’s side, but he will not be involved in Saturday’s Premier League clash with Crystal Palace.
“Since allegations were first made in June, Antony has cooperated with police inquiries in both Brazil and the UK, and he continues to do so,” a United statement read.
“As Antony’s employer, Manchester United has decided that he will resume training at Carrington, and be available for selection, while police inquiries proceed.
“This will be kept under review pending further developments in the case.
“As a club, we condemn acts of violence and abuse. We recognise the importance of safeguarding all those involved in this situation, and acknowledge the impact these allegations have on survivors of abuse.”
Antony is facing several accusations of physical aggression towards his former girlfriend Gabriela Cavallin, who spoke to Brazilian media earlier this month.
The winger has denied those allegations, as well as further assault claims made by two other women.
He has not been arrested or charged in either Brazil or in Britain and he left the voluntary interview, where he presented evidence to support his strenuous denials, without any restrictions.
Antony joined United from Ajax last year for an initial fee of 95 million euros ($101 million).
He has struggled to perform consistently, scoring just eight goals in 48 games.
AFP
