But Klopp will ensure there is no complacency in his side when Moyes' boys come to town.
No side in the land boasts a greater pedigree in this competition, with the Reds having won it nine times in their illustrious history.
Most recently they triumphed over Chelsea in the 2022 final, Kepa Arrizabalaga memorably being brought on only to sky his crucial penalty over Caoimhin Kelleher's crossbar.
West Ham face a tall order on Wednesday night, with Liverpool having previously won every game in all competitions at Anfield this term, prior to the Man Utd stalemate last weekend.
They may be boosted by the Reds having one eye on Saturday evening's top-of-the-table showdown with Arsenal, however.
Klopp named a mixed side in the last round against Bournemouth, although star man Mo Salah did start against the Cherries.
The German will have big decisions to make in his team selection this time around - needing to get the balance right between respecting West Ham's threat and wanting his star players to be fresh for the weekend.
West Ham proved their cup pedigree last season by winning the Europa Conference League.
And boss Moyes would surely love nothing more than to add to his trophy cabinet once again this term.
What is their form like?
Liverpool have had to dig deep on a number of occasions in recent weeks.
The Reds scored two late goals to break Fulhamhearts and beat them 4-3 at Anfield on December 3.
A 2-0 win at struggling Sheffield United followed, before another late double saw them complete a further escape act by beating Crystal Palace 2-1.
Last mid-week a much-changed side lost 2-1 to Union Saint-Gilloise in a Europa League dead-rubber in Belgium.
Then on Sunday they failed to break down Man Utd, drawing 0-0 at Anfield.
As for West Ham, one result in particular sticks out like a sore thumb in recent weeks.
They secured a magnificent 2-1 win at Tottenham on December 7, and have also beaten Freiburg and Wolves since.
Bizarrely, however, they lost 5-0 at Fulham in among that run of results, a performance Moyes will never want his side to emulate.
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Liverpool were frustrated by Man Utd on SundayCredit: Rex
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Mohammed Kudus was the star as West Ham swatted Wolves asideCredit: Getty
Team news
Jurgen Klopp could be without summer signing Ryan Gravenberch after he hobbled off during the Reds' 0-0 draw with Manchester United on Sunday evening.
Alexis Mac Allister was missing from the Liverpool squad on the weekend and will be absent again against West Ham.
Long-term absentees Diogo Jota, Andy Robertson, Thiago, Joel Matip and Stefan Bajcetic will all be unavailable.
For West Ham, they welcomed back captain Kurt Zouma on Sunday, and he will likely start over Konstantinos Mavropanos again in mid-week.
Edson Alvarez returned from an illness, but the game at Anfield will come too soon for strikerMichail Antonio.
Who will be the star men?
Cody Gakpo is yet to show his best form in the Premier League this term, scoring only twice in 15 appearances.
But it's been a different story for the Dutch international in the League Cup, having scored in both previous rounds against Leicester and Bournemouth.
With Saturday's huge clash with Arsenal looming, the likes of of Mo Salah may be rested against West Ham in mid-week.
This could open the door for Gakpo to shine.
Mohammed Kudus has been in red-hot form for West Ham of late.
The summer arrival from Ajax took a while to earn Moyes' trust in the Premier League, but he has been sensational since breaking into the team.
The 23-year-old netted in the last round against Arsenal, and also bagged two in the Premier League victory over Wolves last weekend.
West Ham have an early kick-off against Man Utd on Saturday to think about, but Moyes may be inclined to prioritise the cups again this season and go with a strong line-up, given the brilliant opportunity his side have to reach the semi-finals.
What have the managers said?
Assistant boss Pepijn Lijnders stood in for Jurgen Klopp in this morning's press conference.
He said of Wednesday night's opponents: "West Ham is a team that beat Arsenal and is already in the knockout stages of the Europa League like us.
"They have a lot of technique [in attack], they can create from deep or high, and they can still mix it up with long balls to [Tomas] Soucek.
"I feel they are more aggressive than they were before. Big compliments to the coach [David Moyes] because he's doing a really good job. We will need to be spot on."
Meanwhile, Moyes' No2 Billy McKinlay said: "Going to Anfield is going to be difficult, as it always is.
"But it’s the quarter-finals of the Carabao Cup and a big game for everybody associated with the Club, so hopefully we can go and put in a good performance and the right result."
SunSport prediction
We will learn much more at 7pm when the teamsheets are printed off at Anfield.
Will Jurgen Klopp dare risk Mo Salah ahead of the Arsenal match? Will David Moyes go full strength despite playing Man Utd on Saturday lunchtime?
Going into Wednesday the Hammers appear the more likely team to play a stronger side for the quarter-final clash.
So I'm going to go for an upset, West Ham win.
SunSport predicts: Liverpool 1 West Ham 2
When is Liverpool vs West Ham?
Liverpool vs West Ham will take place TONIGHT, Wednesday, December 20th.
Kick off will be at 8pm GMT.
Anfield will host.
What TV channel is Liverpool vs West Ham on and can it be live streamed?
Liverpool vs West Ham will be broadcast live on Sky Sports Main Event.
Sky Sports customers can live stream all the action via the NOW app.
Alternatively, you can follow SunSport's live blog for all the latest updates from the match.
What are the odds?
Match result
Liverpool - 2/5
Draw - 15/4
West Ham - 6/1
To qualify
Liverpool - 1/5
West Ham - 10/3
*Odds courtesy of Ladbrokes and are correct at the time of publication.
While, on paper, there seems a lot of depth to this Liverpool squad there are some worrying concerns.
Thiago Alcantara is a professional hospital patient, who has had his career blighted by football, Joel Matip the same.
It is no good to the German manager to rely upon players who cannot stay fit for more than a handful of games and may need to invest in the forthcoming transfer window.
With Mohamed Salah heading off to the Africa Cup on Nations also, The Reds will need extra depth.
Jurgen Klopp goes head to head with David Moyes as their two teams look to battle for the final place in the Carabao Cup semi-finals along with Chelsea, Middlesbrough and Fulham.
Liverpool will be without Thiago Alcantara, Stefan Bajcetic, Ben Doak, Andrew Robertson, Joel Matip and Diogo Jota who are all current treatment room attendees.
Despite coming off against Man Utd, Pep Lijnders stated that Ryan Gravenberch could well play this evening, while Alexis Mac Allister also has an outside chance of making his comeback too.
Joe Gomez, Harvey Elliott and Cody Gakpo will all be hoping to get opportunities to impress.
West Ham however, have a fairly empty treatment room with only Michail Antonio as the sole-occupant and is not anticipated to return for another couple of weeks.
David Moyes is expected to stick with Lukasz Fabianski despite Alphonse Areola having returned to full fitness after a wrist injury.
Danny Ings may get the chance to start against his old club as the manager is expected to make changes to cope with their busy fixture schedule over the Christmas period.
Edson Alvarez played the full 90 minutes against Wolves despite having suffered a bang to the hip but he may be rested for tonight’s game.
