Pogba and Martial missed the 1-0 win over FC Astana on Thursday through injury and according to manager Ole Gunnar Solskjaer the pair are unlikely to return in time to feature at the London Stadium.
James has been unable to train since picking up a knock and may also miss out while Luke Shaw is still sidelined with a hamstring problem.
"[Daniel] has not trained the last few days," Solskjaer said. "Hopefully [he might be fit] but not sure.
"We'll have a recovery day with everyone on Friday and we'll see on Saturday. Not really [expecting Pogba and Martial back]. They've not been training yet so I don't think so."
United head to West Ham looking for their first win away from Old Trafford since beating Paris Saint-Germain in March. Solskjaer said teenager Mason Greenwood could keep his place after scoring his first senior goal against Astana.
"It's always hard to keep players who perform well out of the team," Solskjaer said. "If he keeps scoring goals, he'll play.
"If he keeps scoring goals when he's on the pitch he'll get more minutes in the Premier League as well and he'll get his first [league] start soon."
While Greenwood became the youngest United player to score in Europe, Marcus Rashford was guilty of missing a couple of gilt-edged chances.
He has not scored from open play since the 4-0 win over Chelsea on the first weekend of the season but Solskjaer has backed his striker to rediscover his form in front of goal.
"He's getting the chances," Solskjaer said. "Of course he could have had three today.
"The keeper made a few fantastic saves. I don't worry about that, no. We're working every single day in training with Marcus. He wants to improve, wants to be better. It's just one of those days. I thought their keeper was excellent."
Meanwhile, Rashford has said United's exciting young players are already putting pressure on the established stars.
"For me people say 'potential for the future' but if they could see how hard they're working, the future could be very close," Rashford said. "All of us need to keep working hard and they'll get to where they want to be.
"It's not a surprise to me when players come up and they do well. Because of their work ethic, no doubt you'll see them all again."
Greenwood's goal against Astana saw him become the youngest player to score in Europe for United -- eclipsing the record Rashford set against FC Midtjylland in 2016.
It was the 17-year-old's first competitive goal after scoring for the first time in senior football during the summer tour and Rashford is backing the teenager to add plenty more.
"Being a person who's been in his shoes in the past, for him to score that goal I know how he feels," Rashford added. "Even more importantly, it was the goal that won us the game, so I think that's the thing that everybody should be talking about.
"Mason has been doing well since he's joined the first team and 100% there's more to come from him. I'm sure he's excited and everyone else is excited as well. I wouldn't say it's a weight off the shoulders. For kids coming through the academy that doesn't exist, for me.
"They've learned to deal with that [pressure] all the way through their careers, since they were nine years old. Every time they play a game, for other academies Manchester United is the biggest game of their season, so they're used to having pressure to win games."