Pep Guardiola's men, winners of the competition in 2023, sit two points adrift of the 24th and final play-off spot with one match left.
City have it all to do at home to Club Brugge on Matchday 8, with nine out of the expanded 36 teams already out of the tournament.
The reigning Premier League champions know nothing but victory in their final European match will see them finish outside the top 24.
Paris Saint-Germain also remain in danger of being dragged back into the mix despite their thrilling 3-2 comeback win over City last week.
Previously, clubs that finished third out of the old four-team group stage had a chance to qualify for the Europa League knockouts.
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That left only sides that ended bottom without any hope of continuing their European adventure but here's what's changed.
How Champions League elimination works
Failing to qualify inside the top 24 means going out of Europe.
As a result of the expansion, there will be no drop down to the Europa League anymore - even for clubs that lose in the play-offs.
The top eight in the Champions League qualify for the knockouts, with those that finish from ninth to 24th put into a play-off.
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The winners of that two-legged tie will reach the last-16, while the losers will follow teams from 25-36 in exiting Europe entirely.
The teams that finish between 9th and 16th will be seeded for the play-off draw, with the benefit of the return leg being at home.
Champions League: How to follow
All 18 games will be played on Wednesday, January 29.
Kick-off around Europe is simultaneously scheduled for 8pm.
talkSPORT will have live coverage from Aston Villa against Celtic, with Adrian Durham serving as your presenter from the Etihad Stadium.
Commentary will come from Jim Proudfoot and former England captain Andy Townsend.
talkSPORT 2 will also be on hand for City's do-or-die clash with club Brugge, with Ian Danter and Stuart Pearce on the microphone.
talkSPORT.com will also have updates from ALL 18 matches in our dedicated live Champions League blog.
To tune in to talkSPORT through the website, click HERE for the live stream.
You can also listen via the talkSPORT app, on DAB digital radio, through your smart speaker and on 1089 or 1053 AM.
Champions League fixtures
Top-eight guaranteed: Liverpool, Barcelona
Top-24 guaranteed (at least): Arsenal, Inter Milan, Atletico Madrid, AC Milan, Atalanta, Bayer Leverkusen, Aston Villa, Monaco, Feyenoord, Lille, Brest, Borussia Dortmund, Bayern Munich, Real Madrid, Juventus, Celtic
In the balance: PSV, Club Brugge, Benfica, PSG, Sporting, Stuttgart, Manchester City, Dinamo Zagreb, Shakhtar Donetsk
Eliminated: Bologna, Sparta Prague, Leipzig, Girona, Red Star Belgrade, Sturm Graz, Salzburg, Slovan Bratislava, Young Boys
Here, are the full fixtures for matchday eight...
Aston Villa (9th) v Celtic (18th)
Barcelona (2nd) v Atalanta (7th)
Bayer Leverkusen (8th) v Sparta Prague (29th)
Bayern Munich (15th) v Slovan Bratislava (35th)
Borussia Dortmund (14th) v Shakhtar Donetsk (27th)
Brest (13th) v Real Madrid (16th)
Dinamo Zagreb (26th) v AC Milan (6th)
Girona (31st) v Arsenal (3rd)
Inter Milan (4th) v Monaco (10th)
Juventus (17th) v Benfica (21st)
Lille (12th) v Feyenoord (11th)
Man City (25th) v Brugge (20th)
PSV (19th) v Liverpool (1st)
RB Salzburg (34th) v Atletico Madrid (5th)
Sporting Lisbon (23rd) v Bologna (28th)
Sturm Graz (33rd) v RB Leipzig (30th)
Stuttgart (24th) v PSG (22nd)
Young Boys (36th) v Red Star Belgrade (32nd)