The winger limped out of the quarterfinal victory over PSG with a calf injury, and is yet to train with the squad ahead of Tuesday's match.
The winger limped out of his side's quarterfinal second-leg victory over Paris Saint-Germain with a calf injury and looks set to miss the meeting with Diego Simeone's men as well.
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 travels to bottom-of-the-table Sunderland with renewed belief in its title bid.
A Connor Wickham double saw the Black Cats hold Manchester City to a 2-2 draw 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 honors at the business end of the season. Thankfully we are."