The Sweden international missed out against Atalanta BC in the Champions League on Tuesday due to a knock that he picked up during a training session on Monday.
Solskjaer, speaking during Friday's pre-match press conference, claimed that the centre-back is "still a doubt", but the Norwegian is 'expecting' him to be available for selection.
"Lindelof? He's still a doubt, but hopefully, he can come back in tomorrow and say that he's ready. I would expect him to be ready, to put it that way, but I can't promise you," Solskjaer told reporters.
However, Varane is set to be on the sidelines for the next month with a hamstring problem, meaning that Eric Bailly, who started against Atalanta, could be in line for his first league appearance of the campaign in the Manchester derby.