Roberto Mancini's expensively-assembled English champions face elimination from the group stages for the second successive season following two defeats and a draw from their opening three Group D matches.
Their latest European adventure ended in a conclusive 3-1 defeat in Amsterdam two weeks ago and that result, together with a 3-2 defeat at Real Madrid and a 1-1 home draw with Borussia Dortmund, has left their future in the competition dangling by a thread.
Dortmund lead the way with seven points followed by Real who have six and Ajax (three). City (one) will need to improve their game significantly to overtake the sides ahead of them and reach the last 16 - and that is if other results go in their favour.
City have also looked unimpressive in their last three Premier League games against West Bromwich Albion, Swansea City and West Ham United where they drew 0-0 on Saturday and although they are the only team still to lose in the top flight, they have rarely played like champions.
Mancini said after the goalless draw at Upton Park that his team needed to recapture the attacking verve which helped them clinch last season's league title.
"We missed so many chances against West Ham and when you miss these kinds of chances you cannot expect to win," he explained.
"We have improved our defensive play but we need to start scoring like last year and I think we need to improve our offensive play."
A MIRACLE
Mancini, who has lost the services of injured defender Micah Richards for a month with a knee injury, has already said his side need "a miracle" to qualify from their group.
The only thing in their favour is that Ajax have stumbled in recent matches since beating City on October 24.
Ajax travel to Manchester hoping that a repeat of their stunning 3-1 home win, when Siem de Jong, Niklas Moisander and Christian Eriksen scored, will put their Dutch league woes behind them.
Frank de Boer's men have taken three points from the last three domestic fixtures and they lost for the first time this season when they were beaten 2-0 at home by Vitesse Arnhem on Saturday.
Despite that defeat, and even though they are still without injured striker Kolbeinn Sightorsson, De Boer believes Ajax can turn the tide.
"We lacked aggression in the last match and didn't play the way we can but I am convinced that it will be different on Tuesday," said De Boer.
Possible teams:
Manchester City: 1-Joe Hart; 13-Aleksandar Kolarov, 4-Vincent Kompany, 6-Joleon Lescott, 22-Gael Clichy; 7-James Milner, 42-Yaya Toure, 18-Gareth Barry, 32-Carlos Tevez, 8-Samir Nasri; 16-Sergio Aguero.
Ajax Amsterdam: 1-Kenneth Vermeer; 24-Ricardo van Rhijn, 3-Toby Alderweireld, 4-Niklas Moisander, 17-Daley Blind; 5-Christian Poulsen, 10-Siem de Jong, 20-Lasse Schone; 19-Tobias Sana, 8-Christian Eriksen, 49-Ryan Babel.
