The Brazil star has made just one appearance this season as an 89th-minute substitute at Brighton, and will be hoping to get his first start in the Carabao Cup third-round tie against Barnsley at Old Trafford on Tuesday night.
'Tomorrow you will see what the line-up will be,' said Ten Hag, who has preferred Marcus Rashford, Amad Diallo and Alejandro Garnacho on the wings in the opening five games of the season.
'We have training every day and the players have to earn the right to play. When players do the right thing in training and the attitude is good, and when they show performance in training then they will earn the right to play.'
Ten Hag won the Carabao Cup in his first season at Old Trafford and dismissed suggestions that new co-owners Ineos will have their sights set on greater prizes.
Erik ten Hag has told Man United winger Antony (left) that he must earn the right to play
'I wouldn't say it's insignificant,' added the Dutchman. 'The FA Cup and Carabao Cup, they're significant. I see the attention from all the teams, all the owners, all the managers.
'When they win the trophies like Liverpool last year, and I see all the teams battling for it, we want the same. In football, to win trophies it's very important. You have five opportunities and our aim is to win all the games if possible.'
Antony signed for £86m two years ago but has been criticised for his performances since joining United.
Last season, he scored just three goals - including one against League Two side Newport County in the FA Cup - and made two assists in 38 appearances in all competitions.
The 24-year-old has also endured a turbulent time off the pitch after he was accused of domestic abuse by three women last year, but he was not arrested or charged in either Brazil or the UK and he denied the allegations.
A Brazilian police investigation into the allegations concluded last month without any charges being brought, but prosecutors could still look into the claims.
Antony's lawyers said in a statement: 'The defence of player Antony Matheus dos Santos, in light of the news published by the press this Tuesday (20 August 2024), hereby confirms that the police investigation opened at the fifth Women's Defense Precinct of Sao Paulo, of the Civil Police, was closed without any police indictment.
'The defence has always believed that the investigations, that run under confidentiality, would prove Antony's innocence.'
Antony and his girlfriend Rosilene Silva had reason to celebrate during the international break as they announced their engagement via Instagram.
Antony and his childhood sweetheart - who have known each other since their school years in Sao Paulo - uploaded a joint post featuring three photographs.
One of the pictures showed the 24-year-old footballer proposing on bent knee. Another featured Antony kissing his bride-to-be on her cheek.