The Citizens lost 2-0 to Tottenham Hotspur at the weekend and are down in 13th in the Premier League, but they have won three from three in Europe to top Group C.
Not since 2008-09, long before Pep Guardiola's arrival, have City had as few as 12 points from their opening 12 Premier League matches.
The Citizens' tally of 10 goals scored, meanwhile, is the fewest they have managed since 2006-07 when finishing 14th under Stuart Pearce.
City may be an entirely different club now, but they have certainly not started the campaign like a European powerhouse and Guardiola needs to get a response out of his players.
The good news for the Catalan coach, who signed a new two-year deal last week, is that progress to the last 16 of the Champions League looks pretty routine from this point.
City defeated Porto 3-1 in their opening group match and have brushed aside Marseille and Olympiacos by the same 3-0 scoreline, giving them nine points from nine.
A point against Greek champions Olympiacos on Wednesday should be enough to see City through with two games - away to Porto and home to Marseille - still to play.
Olympiacos ideally need a victory to keep alive their slim hopes of progressing, having lost to Porto and Man City in their last two games without scoring.
Pedro Martins's side did beat Marseille 1-0 in their opening match, though, and they were not as bad in the reverse meeting with City as the scoreline suggests.
Indeed, speaking after that game, Martins said: "If we can play like we did in the second half, we can get something more out of the next encounter."
Olympiacos have only won one of their last eight games against English teams in European competition, but that lone victory came against Arsenal in February.
This will be City's first away game against a Greek opponent since February 2011, meanwhile, when they drew 0-0 with Aris Thessaloniki in the Europa League.
Olympiacos Champions League form: WLL
Olympiacos form (all competitions): WLWLWW
Manchester City Champions League form: WWW
Manchester City form (all competitions): DWWWDL
After making his return from injury as a substitute in the loss to Tottenham, Raheem Sterling is in contention to start this match.
Striker Sergio Aguero watched on from the bench for the full 90 minutes, but this might present Guardiola with an opportunity to ease him back into the side.
Ferran Torres has scored in each of his first three Champions League appearances for City, and could become only the third player to score in four consecutive games for the club.
Olympiacos possible starting lineup:
Sa; Drager, Semedo, Cisse, Rafinha; M'Vila, Bouchalakis, Camara; Randjelovic, Fortounis, Masouras
Manchester City possible starting lineup:
Ederson; Walker, Dias, Laporte, Cancelo; De Bruyne, Rodri, Gundogan; Sterling, Aguero, Foden
We say: Olympiacos 0-2 Manchester City
Man City are looking to win their opening four Champions League group games for the second time under Guardiola, three years on from last achieving that feat.
The visitors have won their last two games in the competition without conceding and, despite their disappointing domestic form, we can see them extending that run on Wednesday.