Martial, who missed the first two games of the season with a hamstring problem, is sidelined after he suffered an achilles injury during a substitute appearance in the 2-1 win over Liverpool.
“Casemiro is fit. He did all the training sessions, he trained individually and the last days with the team,” Ten Hag told a news conference on Friday.
“Anthony Martial is not fit. He came out with a problem on his Achilles out of the game. We have to wait. I cannot tell the prognosis, I hope he will be available for the next game [against Leicester City].”
Sources have told ESPN that the club are still chasing Ajax winger Antony, and Ten Hag said the club could spend again before the transfer deadline on Sept. 1.
“We need players, it is clear, but we need the right players,” the United manager said.
“The whole transfer window, we are happy with what we did until now but the bar has to be high.”
United head to Southampton looking for their first away win since February. It was also the last time they won back-to-back games in the Premier League.
“I think in every game there is pressure on the ball and it’s our intention to make the game,” Ten Hag added.
“We need to have a high standard, it’s a demand to the group, to the players. “We have to see the reward and match the runs in and out of possession.
“If you want to dictate the game, you want to do it in possession and out of possession. Organisation has to always be right.”