The trio have missed United's last two games, having sat out of both Sunday's 3-1 win over Newcastle and the goalless draw with Real Sociedad on Thursday night.
Cavani and Van de Beek, who are sidelined with muscle injuries, also failed to make the trip to Turin for the first leg of the Europa League last-32 tie against la Real last week.
Paul Pogba, meanwhile, is still recovering from a thigh injury and is not expected to return to action until March.
United's absences forced centre-half Axel Tuanzebe into midfield on Thursday night and Solskjaer confirmed after the final whistle that he is struggling for options in the middle of the park.
“It’s one of those positions now we suddenly have Scott, Donny and Paul [Pogba] out," he said.
"We’ve been really well off before and now we might have to look at options because I’m not sure if any will be available.
”Scott, Donny and Edinson - we hope that they can be available for the weekend, but I’m not sure. Paul is still out for a few weeks unfortunately.”
Daniel James came off midway through the 0-0 draw with Sociedad carrying an injury which will be assessed before the trip to Stamford Bridge.
“He felt a tweak," the United manager said of James. "With the intensity he works at he felt something, so we hope it’s not really serious.
"We’ll have to check on him. It gave Amad a chance to have half an hour-ish.“