The winger limped out of the Champions League quarter-final second-leg victory over PSG with a calf injury, and is yet to train with the squad ahead of the semi-final first leg
The double player-of-the-year nominee limped out of last week's quarter-final second-leg victory over Paris Saint-Germain with a calf injury.
Chelsea assistant manager Steve Holland said earlier in the week that Hazard should be available again "sooner rather than later", but Friday's update is far more negative.
"Hazard is not definitely out for Tuesday but he hasn't trained with the squad yet which means he's a major doubt," Holland told reporters.
Before the clash at the Vicente Calderon, Chelsea travel to bottom-of-the-table Sunderland with renewed belief in their title bid.
A Connor Wickham double saw the Black Cats hold Manchester City to a 2-2 draw on Wednesday, meaning the Blues can now claim the title if they win all of their remaining games.
Holland continued: "First, second and third position are possible for all three teams at the top. It is very close. This is a club that is used to playing a lot of matches at this stage of the season.
"It is a really challenging period, not just physically - that's obvious - but emotionally too. I think experience is always vital in any competition. We have a good blend in our squad.
"This game tomorrow is of huge importance. I don't believe the title will be decided by our match with Liverpool. Tomorrow will be a very difficult game that we have to approach in a very professional manner.
"The objection for this club is to be competing for major honours at the business end of the season. Thankfully we are."