Lingard excelled in the 2-1 victory over Manchester City last Saturday, but has been unable to train since, due to a knock picked up during the match.
Solskjaer also revealed that he expects Paul Pogba, Eric Bailly and Tim Fosu-Mensah to begin participating in full training with the first team from next week onwards.
“I'm not sure about Jesse, but I hope [he can feature],”
Ole told reporters, after the Reds had secured top spot in Europa League Group L with a 4-0 victory over AZ Alkmaar.
“He wasn't training today, but we'll check him on Saturday probably.