United manager Solskjaer expects forwards Edinson Cavani and Anthony Martial to be fit, the former having missed seven of United's last eight matches and the latter having limped out of the 1-1 first-leg draw against Milan with a hip problem.
Donny van de Beek, who has been sidelined since 22 February, may also be ready to return, while Paul Pogba – who last played in the 3-3 Premier League draw with Everton on 6 February – could also be back in the squad.
With Marcus Rashford having returned from ankle trouble in the 1-0 Premier League win over West Ham and David de Gea now free to return after self-isolating, United could look in much better shape for the return fixture at San Siro, where the tie is poised at 1-1.
"Injury-wise, I hope that we have four or five players back for that game," Solskjaer said after the win over West Ham. "We hope, or it's very likely that Edinson and Anthony are fit. Donny, hopefully as well. Paul even might make the trip. David is back from isolation.
"That's more numbers. Today, we even had two goalkeepers on the bench, so we need them back."
United's hard-fought win over the Hammers, earned through a second-half own goal from Craig Dawson, lifted the Red Devils back into second in the Premier League table.
While they are 14 points behind leader Manchester City with a game in hand, they now have a nine-point cushion to West Ham in fifth, putting them in a strong position at least for a top-four finish.
Solskjaer was delighted with the attitude his players displayed three days on from conceding an injury-time equaliser to Milan, even if the performance was not quite up to scratch in attack.
"It's been a big week for us. We're starting to build some momentum in the league. We've opened the gap further to West Ham, which was important to us," he said.
"We want to improve on last season. We want to get to a final, we want to move up the table. This week was always going to be massive. The reaction after the late equaliser that Milan scored was really good because you never know how that can affect you.
"It looked like everyone wanted to show what they could do, the first 15, 20 minutes, maybe a little bit too eager, lacked a bit of composure. The attitude was spot on, When we got the composure, we built more and more pressure and momentum.
"We had to readjust a little bit. After 15, 20 minutes, there was a break in play and we just had to get to grips with our composure. We kept firing passes into each other and couldn't find a red shirt whatsoever.
"We've had four clean sheets now [in a row] and that's always the foundation. We want to score goals, we're creating big chances. I feel we're getting back to what we can. It's only a week ago we beat City 2-0, so I don't want to be greedy. Nobody can score four or five goals in every game in the Premier League. You've got to earn it. We always back our players to score enough goals."
Mason Greenwood performed well as the central striker but was unable to end his goal drought, with Lukasz Fabianski making a fine save to deny him in the first half before he smashed a shot off the post in the second.
The 19 year-old has only scored once in 23 league games this season, having managed 10 in just 12 starts in 2019-2020, but Solskjaer is not concerned.
"His performance was really good, he deserved a goal," said the United boss. "He's played really well lately. He linked the play well for us, he held it up for us, and he had our two best chances, a great save by Fabianski and unfortunately, he hit the post on the second one.
"He kept creating chances for others as well. I'm very pleased with Mason at the moment."
United has kept four straight clean sheets in the Premier League for the first time under Solskjaer, last doing so in January 2018 when Jose Mourinho was at the helm.
Solskjaer's United has only lost one of its last 23 Premier League games (W14 D8), this after suffering three defeats in its opening six games of the season.