Forrest has not played since the 2-0 defeat to Kilmarnock on 27 October and is now in a race against time to be ready for the visit of the Russian side on 5 December.
Celtic must better Benfica's result away to Barcelona in the final group game in order to qualify for the last 16.
Lennon said: "James Forrest had a scan on Monday and it has come through that he has got a tendon problem in the hamstring area.
"It always seems to be a complication with James, none of his injuries seem to be straightforward. We hope, and it's an outside chance, he'll be fit for Spartak."
Forrest will miss Saturday's home game against Inverness with Thomas Rogne (calf), Scott Brown and Joe Ledley (both hip) and Charlie Mulgrew (illness) all doubtful.
Lennon also revealed he would rest players ahead of the Spartak game after feeling fatigue was a problem in Portugal during Celtic's 24th competitive match of the season.
He said: "I'm going to have to use the squad for these upcoming games. We need players who haven't played as much as they would like to really come to the fore and make sure our league form is consistent, so we go into the Spartak game ready to go."