After a series of disappointing results, Roberto Mancini's men now have only a mathematical chance of progressing to the knockout stages.
City have collected just two points from their opening four Group D matches and must win both their remaining fixtures - and hope other results go in their favour - to avoid premature elimination for a second successive year.
There are numerous permutations but the challenge facing City would seem an improbable one and manager Mancini has more or less admitted as much.
"It is finished," the Italian said. "I always believe in my team but now I think it is very difficult.
"We have two more difficult games left, which we have to try and win."
Nevertheless, the visit of nine-times European champions Real to the Etihad Stadium on Wednesday will be a glamorous occasion for the Barclays Premier League winners.
Prior to this weekend's clash with Aston Villa, Mancini had to try to contain any excitement.
"We cannot let minds wander to Real Madrid in midweek," Mancini said.
But he added: "That will be a great game, I am sure."
Former Manchester United star Cristiano Ronaldo scored a late winner as City were beaten 3-2 by Real in a thriller at the Bernabeu in their opening match of the campaign.
They hoped to build on what was largely a positive performance but could only manage a 1-1 home draw with Borussia Dortmund and then lost 3-1 to Ajax in Amsterdam.
Last week's 2-2 draw with Ajax in the return match at Eastlands was controversial, with City having a late goal disallowed and an injury-time penalty declined, but it all but ended City's hopes.
As the bottom side in a tough group comprised of domestic champions, City even face a fight to claim a consolation spot in the Europa League.
Despite that, the players have not yet written off their prospects.
Midfield talisman Yaya Toure said: "We have to continue to work hard.
"We have a couple of chances against Real Madrid at home and go to Dortmund. We have a chance to qualify. We have a fantastic squad."
City wrap up their group programme with a trip to Dortmund on December 4.
Like City, the Germans under-performed in the competition last season but have excelled this time and currently top the group.
A home win over Real and a draw at the Bernabeu have taken Dortmund to eight points, one above the Spaniards. Ajax are third with four.