City threw away a 5-3 first leg lead, going down 3-1 away to Monaco last night.
The Ligue One leaders progress by virtue of their first leg away goals.
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Joining Monaco in tomorrow's quarter final draw is Atletico Madrid.
They had keeper Jan Oblak to thank for a string of saves in their scoreless second leg with Bayer Leverkusen.
Atletico won through 4-2 on aggregate.