United are currently 10th in the early season Premier League table with six points from four matches. They bounced back from consecutive losses at Brighton (2-1) and at home to Liverpool (3-0) to win 3-0 at Southampton on Saturday.
But Ten Hag was coy when asked about the possibility that Antony, who has made just one appearance as a late substitute at Brighton so far this season, starting against Barnsley.
"You will see what the line-up will be (on Tuesday)," he replied. "We have everyday training and the players have to earn the right to play," he told reporters on Monday.