Wales' Lydiate, 28, collided with team-mate Aaron Jarvis in a 12-7 win over Newport Gwent Dragons on 1 January.
But Ospreys have registered scrum-half Rhys Webb in their European squad in place of young wing Dafydd Howells.
Webb - who has not played since injuring a foot while playing for Wales on 5 September - is not expected to play against Exeter, but is eligible.
Ospreys are hopeful that Webb will return by early February.
Fly-half Dan Biggar and hooker Scott Baldwin, who both left the pitch with dead legs during the win over Clermont last Friday, are said to be ready for Sunday's game.
However, on Lydiate's fitness, backs coach Gruff Rees said he was "touch and go".
"We have to do what's right, despite the magnitude of the game," Rees added.
A win against Exeter would secure Ospreys' passage to the quarter-finals.
Ospreys flanker Dan Lydiate is a doubt for Sunday's crucial Champions Cup Pool Two match against Exeter.