Manchester United and Real Sociedad will square it out in the first leg of their Europa League tie on Thursday.
The pair have suffered muscle injuries and Solskjaer has confirmed that they will not travel to Italy with the rest of the squad.
Speaking at his pre-match press conference, Solskjaer also revealed that Paul Pogba will be out of action for the remainder of February as a result of the thigh injury he suffered in United's 3-3 draw with Everton.
Solskjaer said: “Paul's recovering. He's starting the treatment.
“It'll still be a few weeks, he won't be playing in February that's for sure.
“Donny and Edinson are injured unfortunately, muscle injuries, so they won’t travel.
“Apart from that, we have a couple of doubtful ones, if they'll be fit enough – Anthony [Martial] and Scott [McTominay].”
The first leg of United's tie with Sociedad is being played in Turin as a result of coronavirus.
Teenage prospects Amad and Shola Shoretire will also be part of the travelling squad.
This article was most recently revised and updated 2 years ago