Defeat for City at home to a young and vibrant Ajax side, who beat them in Amsterdam a fortnight ago, would signal a second successive group stage exit of Europe's premier club competition and heap pressure on manager Roberto Mancini.
Mancini, who must deliver something of note on the European front for owner Sheikh Mansour bin Zayed Al Nahyan after his huge investment in players, will also be hoping no-one emerges victorious from the other game where Real Madrid host German champions Borussia Dortmund.
Dortmund top the group on seven points with Real a point behind and City are bottom six points adrift of the table toppers after three games.
Arsenal have more room for manoeuvre as they too seek to avenge defeat when they travel to play Schalke 04 as the Gunners lie second three points ahead of Greek outfit Olympiakos.
However, Olympiakos have an enticing home clash with ailing French champions Montpellier and will be expecting at the very least to maintain the pressure on Arsene Wenger's team.
Elsewhere the two teams with 100% records, Porto and the surprise packages of Malaga are both away with the former playing Dynamo Kiev and the Spanish side away at Italian giants AC Milan.
Mancini realises that victory on Tuesday is imperative.
Whilst the Italian is satisfied with the improvement in his defence of late he is less happy with his much-vaunted strikeforce, who have been misfiring and scored just once in their last two league games against minnows Swansea and West Ham.
"We have more chances to go through (in the Champions League)," said the 47-year-old.
"It's important we finish in the group stage well.
"What the Ajax scouts think of us I don't know, it's not important; what the players think is."
While City are unbeaten in 18 home matches in European competition Ajax can travel in some hope as they beat City's neigbours Manchester United 2-1 at Old Trafford in their Europa League Last 32 clash there last season.
Real go into their game with Dortmund on the back of having given coach Jose Mourinho his 100th victory of his reign there with a 4-0 win over Real Zaragoza.
Mourinho, who is bidding to become the first coach to win the trophy with three different clubs, said Real just needed maximum points from their remaining two home games to seal their place in the knockout round.
"We are second. Everyone knows that there are groups that are jokes and that this is 'the group'.
"We are in a good position to progress. If we win the two home matches that we have left they are six points that are well within reach and could be enough to get through to the second round."
Schalke may have lost on Saturday but their players were not in the least dismayed as they prepared to welcome an Arsenal side that has made their worst start to a Premier League season since Wenger took charge in 1996.
"I think we have every chance. We won in London, why shouldn't we succeed in front of our own fans?" said their 24-year-old captain Benedikt Hoewedes.
"We will not be thrown off by a defeat."
Milan may look back and see this as the week that turned their season round if they can follow up the Chievo thrashing by inflicting Malaga's first defeat of the Champions League group stage.
They will be looking to their 'little Pharaoh' Stephan El Shaarawy to continue his superb scoring spree which has more than made up for Swedish striker Zlatan Ibrahimovic's departure in the summer.
The 20-year-old - son of an Egytian father and an Italian mother - is well on course for a new target set for him by club captain Massimo Ambrosini with the latter having already promised to pay for his winter holiday for scoring seven goals by December in all competitions.
"He has earned his winter vacation, but if he scores ten goals I'll pay for him to take a tour of the Caribbean," Ambrosini told uefa.com