Lingard, 26, injured his hamstring in the Champions League defeat by Paris St-Germain 10 days ago and was expected to be out for up to three weeks.
France forward Martial, 23, could also return from the groin injury he picked up in the first half against PSG.
“Jesse is looking OK. I hope with Anthony,” said Solskjaer.
“Anthony’s was a different muscle, so we think he might be ready and hope that Jesse will.
“We’ve got two more days so they’ve got to get through these two sessions. They’ve not been part of training yet but they’ve been doing some recovery work.”