The forward has not played for United since the first week of September and was withdrawn from Brazil's squad for two World Cup qualifying matches amid police investigations into assault allegations made by his former girlfriend Gabriela Cavallin.
Antony has denied any wrongdoing.
Last week, the Premier League club confirmed that Antony would resume training. The club had earlier agreed to allow the Brazilian to take a period of absence.
"Antony will be in consideration. Yesterday was his first time back in team training. We have final training and then we make a decision," Ten Hag told reporters ahead of Tuesday's home game against Turkish champions Galatasaray.
Ten Hag also confirmed that Argentine Lisandro Martinez would have to undergo surgery for a foot injury. The United defender has been ruled out of action for an extended period, after aggravating an injury he suffered in April.
United go into their game against Galatasaray off the back of a 1-0 loss to Crystal Palace on Saturday which dropped them down to 10th in the Premier League standings.
It was their fourth league defeat of the season - making this their worst start to a top-flight campaign since 1989-90.
Despite United's recent struggles, Ten Hag said his team were "moving forward", adding: "You have to make adjustments. We don't have a full back on the left side. There are shortages in our game.
"A lot of positives, but at the end of the day it is about results and we didn't get it."
United are bottom of Group A in the Champions League, after a 4-3 defeat at Bayern Munich in their opening match last month, but defender Raphael Varane said they possessed the quality to win the Champions League.
"You need to be efficient to win trophies. We have the quality in the squad to win competitions. We have to move forward and improve," Varane told reporters.
"The competition is difficult, you have to take care of every detail but we have a team of quality, of good mentality.
"We have to make some improvements, it was not the start to the season we expected but I still believe we have the quality to compete with the best teams in the world."
