While the Cityzens have gone on to lift silverware in four consecutive seasons, the closest West Ham have got to a serious trophy was 15 years ago when they lost to Liverpool in the 2006 FA Cup final.
The Irons are playing well and their supporters would love nothing more than a long-awaited cup run...although it's arguable whether they'd actually want it in this competition now they are in Europe.
Though their main problem in the Carabao Cup is City stand in their way, are firing on all cylinders and look simply unbeatable.
When, where and how to watch
When: Wednesday, October 27, 7:45PM BST
Where: London Stadium
How to watch: Not televised in the UK
Best bets in West Ham vs Man City
Six wins from nine games, five clean sheets and just three goals conceded. No, we're not talking about City - this is West Ham's recent record.
David Moyes is enjoying a brilliant start to the season but what exactly can the Scot realistically achieve with the Hammers this season?
Another top six finish perhaps? Another appearance in the Europa League? While both those outcomes are desirable, West Ham fans would happily sacrifice it all for a trophy.
Considering the level of competition at the top end of the Premier League table, we're not going to see the Hammers lifting the league crown. Winning the Europa League also seems like a long shot - despite their promising start.
The Carabao Cup though, could be the one. West Ham have already eliminated Manchester United in the earlier round. Who's to say they couldn't take out another Manchester outfit this Wednesday night and bag a place in the quarter-final.
Yes, Man City are on another level and over the course of the season they are undoubtedly the better side. However, this is not a season. This is simply a one game shootout.
Every stat may be in favour of the defending champions but with West Ham high on confidence and playing in front of their home crowd, they're our bet in the outright market.
Last three meetings
Man City 2-1 West Ham (Premier League - February 27, 2021)
In their previous meeting, City were given a tough challenge but ultimately, they prevailed thanks to some unlikely goal getters.
Ruben Dias opened the scoring in the 30th minute before City were pegged back by a Michail Antonio equaliser.
In the second half, John Stones bagged the winner as all three points stayed at the Etihad stadium.
West Ham 1-1 Man City (Premier League - October 24, 2020)
The last encounter between these sides at the London stadium ended all square.
Antonio put the Hammers ahead in the 18th minute before Phil Foden replied with a goal of his own in the second half.
Man City 2-0 West Ham (Premier League - February 19, 2020)
The Citizens were a lot more clinical when they met West Ham in the early weeks of 2020.
Last 10 head-to-heads
West Ham wins: 0
Man City wins: 9
West Ham goals: 4
Man City goals: 30
Masters of the Carabao Cup
Man City love this competition. They love it as much as Paul Scholes loves toenails. They probably love it more than David Beckham loves Qatari money. Okay, maybe not.
Nevertheless, City's incredible run has to be underlined with some numbers. So here they are.
Since the 2013/14 season, Guardiola's men have only lost two games in this competition. The two clubs who beat them during this run are Manchester United and, strangely, Newcastle United. Overall, City have won six of the last eight editions of the Carabao Cup, including the last four.
City will not relinquish their league cup dominance without a fight. And while we did tip West Ham to win, you better believe it's going to be closely contested.
With that in mind, we're backing the match to be won by a one goal margin.
Is Man City's defence really that impervious?
Only three points separate West Ham and Manchester City in the Premier League table. Yet the most interesting comparison comes from the goal difference column.
Both sides have scored a similar number of efforts with City bagging 20 goals and the Hammers registering 16.
When it comes to the defence, that's when things begin to change. City currently boast the Premier League's second-best defence having conceded four goals. West Ham, meanwhile, have allowed 10.
There is a slight caveat though. Moyes' men have significantly improved at the back if you look at the last few weeks. In fact, West Ham have picked up four clean sheets from five games. In the same space of time, Man City have only done that once.
City's defence is not impervious. In fact, they are more penetrable than you might think. RB Leipzig, for instance, put three past them back in September. Club Brugge and Brighton also found a way through.
We know City can score but recent information also tells us that they are capable of a slip up at the back from time to time. With that in mind, both teams to score is our third betting selection.
West Ham have scored two goals in their last two games against Man City. No prizes for guessing who scored them both.
Michail Antonio is a man on fire this season and there's no reason why he couldn't maintain his scoring run against the Cityzens.
At around the 13/5 mark, he's going to be a popular man among the punters.
From a Manchester City perspective, backing a goalscorer is a complete lottery. With that in mind, we might as well go for someone with a decent price.
Jack Grealish certainly fits that bill at 9/5. The England international has scored three goals in his last six Carabao Cup appearances. Now that's a run we can get behind.