The France international has struggled with a number of injury problems early in the season, and his latest issue, which is related to his back, has kept him out since October 9.
Martial has missed Man United's last four Premier League games against Newcastle United, Tottenham Hotspur, Chelsea and West Ham United, in addition to the Europa League matches with Omonia and Sheriff Tiraspol.
The attacker has only made four appearances for the Red Devils this season, but he has impressed during his limited outings, scoring three times and contributing two assists.
Martial missed the start of the campaign with a hamstring issue, while he was absent between the end of August and start of October due to an Achilles problem.
Speaking ahead of Sunday's Premier League clash with West Ham United, Red Devils boss Erik ten Hag said that he was 'hopeful' the forward could play before the 2022 World Cup.
"I hope [so]. But he is making progress. He is outside and he is working there. So, he is on the pitch, and we are waiting for his step back into team training," Ten Hag told reporters.
"He had a setback against Everton. It was really frustrating for us and also for him. We have seen that he played good in pre-season. He has less minutes [than many other players], but he has scored already three goals.
"At Everton, he had also an important role with the first goal, his assist for Antony, so it would be really good to have him back because he can make a difference. He can score goals but also when linking up he's really important, and the pressing from him is really good."
Martial has now re-joined first-team training, with the former Monaco youngster taking part in the team session on Monday, which could put him in contention for a return against Real Sociedad.
The attacker has only started once for the Red Devils this season, which came against Everton on October 9, but he lasted just 29 minutes, having suffered a back problem.
Martial's three other outings this term have come off the bench, providing an assist as a substitute against Liverpool, before scoring three times in his outings against Manchester City and Omonia.
Man United have another four games before the season breaks for the World Cup, taking on Real Sociedad, Aston Villa twice and Fulham.
The Red Devils will have to make a check on Victor Lindelof and Antony for Thursday's match, with the pair missing out against West Ham due to illness and injury respectively.
Aaron Wan-Bissaka will be battling to be back in the squad after recovering from his recent injury issue, but Brandon Williams, Axel Tuanzebe and Raphael Varane remain in the sidelines.