However, Ten Hag told reporters on Thursday that the 23-year-old's rehabilitation has not gone as well as hoped and he is now set to miss the game against Pep Guardiola's side.
"It is unlikely," Ten Hag said. "There is still a chance but a really small chance. He didn't make progress so he still has a chance but it is unlikely he is available."
Antony's absence would be a further blow for Ten Hag, who is already without Anthony Martial after he suffered a torn hamstring during the final game of the Premier League season against Fulham. Midfielders Marcel Sabitzer and Donny van de Beek are also out, alongside defender Lisandro Martinez.
The injury list has left Ten Hag with decisions to make before naming his side for the first-ever all-Manchester FA Cup final but the Dutchman said he can still pick a team capable of beating City.
"These questions are asked so many times about the absence of players but it is about the players who are available and many times we were successful," he added "We have a good squad and from the good squad we make a good team."
Victory over City would earn the United boss a second domestic trophy in his debut season at Old Trafford. It would also stop City from winning the treble, although Ten Hag said that isn't his main motivation.
"We want to win a cup, it is not about stopping them," Ten Hag said. "I think it is a very good season when you see where we came from and the progress of the team.
"In a tough league like the Premier League and you are third and winning the League Cup and in the final of the FA Cup you can be happy with the season but in summer we start again."