The 28-year-old has not turned out for the Red Devils since the start of December, initially missing a period of football through illness, before it was revealed that had a groin injury which required an operation.
Martial is now back in individual training, as he steps up his recovery, but it remains to be seen when he is cleared to return to full-contact sessions alongside his teammates.
The 28-year-old's contract at Old Trafford is due to expire this summer, and he is widely expected to leave the club on a free transfer in search of pastures new.
When asked whether Martial would play for the club again, Ten Hag said that "it depends on him".
"Martial is back on the pitch as well, but not in the team yet. It depends on him and how quickly is he back and what are the levels. What [he] is showing," Ten Hag told reporters.
Martial's Man United career is coming to an end
Martial has only managed two goals and one assist in 19 appearances for the 20-time English champions this season, and he struggled to make his mark in the first half of the 2023-24 campaign.
The ex-Monaco youngster arrived at Old Trafford in September 2015, and he has represented the Red Devils on 317 occasions in all competitions, scoring 90 goals and registering 50 assists in the process.
Martial has struggled to fulfil his early promise, and it appears almost certain that he will be leaving Man United this summer in search of pastures new.
Transfer expert Fabrizio Romano posted on his official X account on Saturday morning that he was "100% sure" the forward will leave Ten Hag's side when his contract expires.
Ten Hag bemoans Man United's injury problems
Martial's absence has left Rasmus Hojlund as the club's only senior centre-forward, and the team have also had a number of other injury issues this season.
"We [have] missed [Tyrell] Malacia for the whole season. We missed [Luke] Shaw for many games. We lost [Lisandro] Martinez for many, many games. So yeah, [also] Casemiro, Mason Mount," Ten Hag added.
"I know every manager has injuries and you have to deal with it. But I think this season was bad for us in that way and has really had an impact on the way of play and it had a really an impact also on the results we have. But yeah, it's the truth. But I can't think about this. I have to think forward.
"I have to think about the future and how we get this right and how we get those players back. And what is the good news that it looks like players are returning. And so by the end of the season when we go in the final stage, 10 games to go in the league and hopefully two in the cup.
"And then when we can have a squad where [we are] covering all the positions, then it can be a very good end of the season."
Martial is one of three first-team Man United players out of contract at the end of June, with the club also needing to make decisions on the futures of Tom Heaton and Jonny Evans.