With two matches to play former champions Manchester United and Porto and impressive newcomers Malaga are the only teams mathematically certain of qualifying, although the make up of the first knockout round will become clearer this week.
UEFA use a complicated head-to-head and mini-league tiebreak system to work out the final rankings instead of goal difference, meaning uncertainties about who qualifies can last until the final kick of the final match.
But Roberto Di Matteo's men travel without a win in their last four Premier League games and reeling from a surprise 2-1 defeat at West Bromwich Albion on Saturday when defensive lapses cost them the points.
"For some unknown reason November seems to be a bad month for this club," the Italian told reporters.
Chelsea's most important victory in recent weeks came two weeks ago when they beat Shakhtar 3-2 at Stamford Bridge with a last-gasp header from Victor Moses sealing the points and making qualification more likely.
Speaking on BBC TV's Match of the Day this weekend, he told presenter Gary Lineker: "If we had the answer to that we probably would not be where we are.
"But for some freakish reason, we still have a chance in the Champions League and I would like to think that in the two games that are left we can pull off a big surprise and qualify as we still have a chance."
However, Real's French striker Karim Benzema believes his compatriot Samir Nasri is a big threat to the Spanish champions' chances of sealing the victory that could see them through.
