The former Scotland midfielder has been in a race against time since limping out of last Saturday's 1-1 draw at Hibernian with a hamstring injury.
Fellow-midfielder Joe Ledley returned from a month out to play the final 20 minutes at Easter Road but is unlikely to be risked from the start against the Dutch champions.
Left-back Emilio Izaguirre is available having recovered from illness but Lennon must give a late fitness test to right-back Mikael Lustig (hip) before finalising his line-up.
Winger Derk Boerrigter (ankle) and wing-back Adam Matthews (shoulder) miss out through injury while skipper Scott Brown serves the first of his three-match ban following his red card against Barcelona.
Celtic currently prop up Group H with no points and no goals from their opening two matches against AC Milan and Barcelona.
Watch Celtic take on Ajax at Parkhead from 7.30pm on Tuesday, live on Sky Sports 3.