Marcus Rashford is set to travel with the Manchester United squad to West Ham despite aggravating his shoulder.
Rashford came off in the second-half of United's Champions League defeat to Paris Saint-Germain on Wednesday night but trained with the squad on Friday morning.
Luke Shaw has returned to training from a hamstring strain he sustained at Everton four weeks ago but is not fit enough to be available for selection.
"Marcus has been training this morning," Solskjaer said. "Not fully but he's joined in with the group. Obviously, his shoulder stopped him finishing the game, so he's been getting treatment and hopefully he'll be part of the squad that travels, he's having treatment after training.
"Luke's not ready yet, apart from that we had a big squad training again. We're a bit bruised after Wednesday night but hopefully we'll be ready to go again tomorrow."
Supporters will be present at the London Stadium for the Saturday tea-time kick-off for the first time since February 29 as 2,000 West Ham fans are allowed inside under the UK government's Tier 2 criteria.
Greater Manchester is still in Tier 3, so United will not be able to welcome fans back inside Old Trafford for next week's derby but could host 2,000 fans for the visit of Leeds on December 20 - provided the city drops into Tier 2 after its review.
"It'll be great playing in front of fans," Solskjaer added. "We're looking forward to it. Of course, we won't have our fans there but we will just have to use the energy and thrive off the home fans and make them quiet, hopefully. That we make them edgy, we're looking forward to it.
"It's great to see fans back in a stadium, of course we want them back at Old Trafford as well and hopefully we'll get that soon. Football has not been the same."
