The competition is the one major trophy that has so far eluded Pep Guardiola during his time in charge of City.
The Spaniard, who has not won the competition since the second of two triumphs with Barcelona in 2011, is making his fifth attempt to land the piece of silverware the club's owners crave more than any other.
Here, the PA news agency takes a look at City's record in the Champions League, and their exits, under Guardiola.
2016/17 – Monaco (6-6 agg, lost on away goals), last-16
When City replaced Manuel Pellegrini with Guardiola in the summer of 2016 it was widely assumed that they had done so because they felt it would enable them to win the Champions League. Bayern Munich had probably thought along the same lines but the Spaniard could only manage three semi-finals in his three years at the Bundesliga club.
After swatting aside Steaua Bucharest 6-0 over two legs to qualify for the group stages, City reached the knockout rounds by finishing second in a group that included Barcelona, Borussia Monchengladbach and Celtic.
Monaco awaited in the last-16. Leonardo Jardim had a strong squad at his disposal, including a young Kylian Mbappe, a revitalised Radamel Falcao and future City players Benjamin Mendy and Bernardo Silva – but Guardiola's team were expected to win. A topsy-turvy, but wildly entertaining, first leg at the Etihad Stadium saw Monaco lead twice before Sergio Aguero equalised and late goals from John Stones and Leroy Sane sealed a 5-3 victory for City.
Goals from Mbappe and Fabinho saw City's two-goal advantage wiped out before half-time in the second leg, putting the Ligue 1 side in control. Sane struck midway through the second half in the Principality to swing the pendulum back in City's favour but Tiemoue Bakayoko's 77th-minute strike made it 3-1 on the night and saw Guardiola's team eliminated on away goals.
2017/18 – Liverpool (1-5 agg), quarter-final
The 2016/17 season was the first time in Guardiola's managerial career that he had finished a campaign without a trophy. He responded in emphatic fashion with a record-breaking 100-point haul in the Premier League as City were crowned champions alongside their EFL Cup success. However, disappointment in the Champions League continued.
Liverpool were the first team to beat City in the league during the 2017/18 season. Their January success at Anfield saw Jurgen Klopp's side playing high-octane, frenetic football to lead 4-1 after 68 minutes. The game ended 4-3 but it was clear Guardiola would need to adapt when the two teams clashed again in Europe.
For the first leg at Anfield, Guardiola left out Raheem Sterling in favour of Ilkay Gundogan. The conservative move allowed Klopp's effervescent side to target Fernandinho in the holding midfield role, constantly pressing his every touch, and Liverpool led 3-0 with just half an hour on the clock. The tie was virtually over.
Guardiola was accused of overthinking and surprised everyone again in the second leg with a 3-3-1-3 formation – a line-up he had never used at City before. Gabriel Jesus' early goal gave City hope of a miraculous turnaround but Mohamed Salah and Roberto Firmino struck in the second half as Liverpool won again, this time 2-1 at the Etihad.
2018/19 – Tottenham (4-4 agg, lost on away goals), quarter-final
City's domestic dominance continued as they retained the Premier League and EFL Cup, before becoming the first team to complete a clean sweep of trophies in England by also lifting the FA Cup. But, once more, the Champions League proved to be a stumbling block and, again, it was another English team who were City's conquerors.
Guardiola's side were left with work to do after losing the first leg 1-0 in London, where Aguero had seen a first-half penalty saved by Hugo Lloris before Heung-Min Son struck the winning goal 12 minutes from time.
The return game at the Etihad got off to a crazy start as Sterling's double either side of Silva's strike saw City lead 3-2 on the night after only 21 minutes. Son scored both of Spurs' goals – equalising and then putting his side ahead. Aguero put City in front on aggregate just before the hour mark but Fernando Llorente bundled the ball in with his hip after 73 minutes to make it 4-3 on the night and leaving City needing to score again.
In one last extraordinary twist, City thought they had snatched victory in stoppage time when Sterling scored what he thought was his hat-trick goal. However, VAR dramatically intervened, ruling that Aguero was in an offside position as Silva diverted the ball into his path. It meant another painful exit on away goals for Guardiola's team.
2019/20 – Lyon (1-3 agg), quarter-final
Things looked to be changing for City in the Champions League last season. Guardiola's side coasted through a potentially tricky group including Atalanta, Shakhtar Donetsk and Dinamo Zagreb, dropping just four points, and then accounted for Real Madrid in the last-16.
City came from behind to win the first leg in the Bernabeu 2-1 in February with late goals from Jesus and Kevin De Bruyne, before the curtailment of football due to the coronavirus pandemic. City won the return leg in Manchester in August by the same scoreline to advance 4-2 on aggregate.
Due to coronavirus, the remainder of the competition was held in Lisbon as a knockout tournament with one-leg matches, which arguably harmed City's chances. However, a quarter-final draw against Lyon, who had not even qualified for Europe for the following season, gave Guardiola a good chance of getting City to the last four for the first time to set up a tie against his former club Bayern Munich. RB Leipzig, Paris St Germain or Atletico Madrid were potential final opponents, all beatable opposition.
Once more, though, City got it wrong. Guardiola's side were uncharacteristically cautious and fortunate to be level at 1-1 heading into the last 20 minutes of the tie. Two late goals from Moussa Dembele saw the French team go through as City missed a huge opportunity and went out in the quarter-finals for the third year in a row.
2020/21 – Paris St Germain (4-1 agg), semi-final
After a sluggish start to the season, City clicked into gear around the turn of the year as they chased glory on four fronts. It was not until the FA Cup semi-finals came around in April that their hopes of winning an unprecedented quadruple were extinguished with defeat to Chelsea.
They bounced back quickly to win the Carabao Cup for a fourth year in succession with victory over Tottenham in the final and, with a healthy lead in the Premier League, another domestic title looks set to follow.
City reached the Champions League final for the first time with a 4-1 aggregate victory in their semi-final against Paris St Germain. They secured the advantage as they hit back from an early Marquinhos goal to win 2-1 at the Parc des Princes with goals from De Bruyne and Riyad Mahrez.
Mahrez stole the headlines once again with both goals in a 2-0 win in the return game at the Etihad, with PSG's Angel Di Maria sent off six minutes after City's second.
They reached the last four by cruising through a group that included Porto, Olympiacos and Marseille before they saw off Borussia Monchengladbach and Borussia Dortmund in the knockout rounds.