The Reds beat Bournemouth 2-1 thanks to a winner from Darwin Nunez to reach the last eight while the Hammers impressively overcame Arsenal.
David Moyes' side won 3-1 to knock out the Gunners and they'll be aiming to claim another 'Big Six' scalp this week.
Jurgen Klopp has one Carabao Cup trophy in his cabinet and a win here will move his side ever closer to picking up another piece of silverware.
Live commentary: talkSPORT website stream HERE, via the app HERE
Match being broadcast on Sky Sports Main Event and Football
Liverpool: Kelleher, Gomez, Quansah, Van Dijk, Tsimikas, Endo, Szoboszlai, Jones, Elliott, Gakpo, Nunez
Subs: Adrian, Konate, Diaz, Salah, Clark, Gordon, McConnell, Alexander-Arnold, Bradley
West Ham: Areola, Coufal, Mavropanos, Ogbonna, Johnson, Alvarez, Soucek, Fornals, Kudus, Benrahma, Bowen
Subs: Fabianski, Cresswell, Zouma, Paqueta, Ward-Prowse, Ings, Kehrer, Emerson, Mubama
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just nowBy Jack Cunningham
Liverpool 0-0 West Ham
18' - Alvarez feeds Benrahma on the right.
He tricks his way into the box, but Gomez stands firm and shepherds the ball back to Kelleher, who has had nothing to do.
a minute agoBy Jack Cunningham
Liverpool 0-0 West Ham
17' - West Ham come forward through Benrahma.
He initially does well to beat one man before clipping a cross towards the far post that Endo easily heads away.
3 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
15' - Gomez plays a terrible pass back towards Van Dijk.
Bowen is keen, but the big Dutchman snaps in and lashes the ball away, otherwise Bowen is on goal.
4 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
13' - Elliott goes close again!
Nunez wins the ball back inside his half and plays it to Jones.
He dances through the West Ham midfield and rolls a pass to Szoboszlai, he lets it run for Elliott, who cuts in and smashes in a left-footed shot that whistles past the near post.
5 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
12' - Tsimikas swings in a corner from the left.
Ogbonna rises high to crash the ball away, but it feels like a matter of time until the Hammers concede.
7 minutes agoBy Jack Cunningham
Lively start
8 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
10' - Nunez wins the ball back on the left and clips a pass into Tsimikas.
He whips a delicious cross into the area, but there is no one in red there to tap it in.
Proudfoot: "West Ham are struggling to get out."
9 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
9' - Elliott fizzes a shot just wide!
Jones plays a nice pass into the winger, who drives through the middle of the pitch and drives in a bouncing strike that just misses the far post.
10 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
8' - The Hammers are yet to get out of their half in the opening exchanges.
And Liverpool definitely look sharper than they did at the weekend.
12 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
6' - Brilliant from Gakpo to drop deep and find some space.
Nunez makes a brilliant run from left to right and looks to be in, but the flag goes straight up, and he's offside.
However, that looked very tight.
Sweetman-Kirk: "Good play that from Nunez, and maybe the pressure is off him because he's on the left."
13 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
5' - The hosts are lining up with Gakpo through the centre and Gakpo on the left.
They've made a good start here the hosts.
15 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham
3' - Szoboszlai picks up a pocket of space in behind the midfield.
He turns and drives towards goal.
He unleashes a low shot that hits Nunez, and the Hammers clear.
19 minutes agoBy Jack Cunningham
Liverpool 0-0 West Ham - Kick-off
The visitors get us underway
19 minutes agoBy Jack Cunningham
Liverpool vs West Ham
Ogbonna wins the toss but elects not to switch Liverpool around, so the hosts will be attacking the Kop in the second half - as they prefer.
And remember, there is no VAR tonight.
21 minutes agoBy Jack Cunningham
Here they come!
Okay, the teams are out.
The referee is Tim Robinson and we are about to hear 'You'll Never Walk Alone'.
Remember, talkSPORT has live commentary of this one with Jim Proudfoot and Courtney Sweetman-Kirk.
23 minutes agoBy Jack Cunningham
Anfield is ready
Right, Anfield is packed and the teams are in the tunnel.
It can't be understated how big this game is for both sets of teams.
26 minutes agoBy Jack Cunningham
Moyes explains changes
David Moyes has been speaking to Sky Sport about why he's made so many changes ahead of this Carabao Cup quarter-final.
He said: "I am trying to make sure we keep everyone fit and available as we can over this period.
"Nayef Aguerd is ill. Maxwel Cornet and Aaron Cresswell were ill, but the latter felt a bit better."
So it appears as if Lucas Paqueta is simply being rested!
That is very strange, but he's an excellent option to bring off the bench."
29 minutes agoBy Jack Cunningham
Liverpool vs West Ham
We haven't got long to go now, but the Hammers' record at Anfield makes for grim reading.
They've won one of the last 55 meetings.
34 minutes agoBy Jack Cunningham
Warm-ups coming to a close
15 minutes now until kick-off at Anfield and warm-ups are starting to wind down.
38 minutes agoBy Jack Cunningham
Klopp a huge Bowen fan
Jarrod Bowen has long been linked with a move to Liverpool and Jurgen Klopp has potentially just thrown some fuel on the fire.
Speaking to Sky Sports ahead of the match about West Ham, he said: "One of my favourite players, beside my players."
The January transfer window opens soon, so you feel those comments were said for a reason.
40 minutes agoBy Jack Cunningham
Klopp proud of progress
Jurgen Klopp is very pleased with how his new-look Liverpool side is coming along.
Speaking to Sky Sports ahead of the game, he said: "There are a lot of good things that have happened in this first part of the season.
"There are some moments in games where you can see we aren't there yet, but you try everything and take what you can get.
"We want to go through."
45 minutes agoBy Jack Cunningham
Liverpool to make League Cup history
Liverpool have scored 498 goals in the League Cup, and could be the second side to reach 500 in the competition's history after Aston Villa (514).
49 minutes agoBy Jack Cunningham
Support for Nunez
Since Darwin Nunez scored in a 2-1 Carabao Cup win over Bournemouth, he hasn't got a goal since.
That's ten matches in all competitions without one.
But despite this, there does seem to be a recognition that he's enjoying a better season and Liverpool assistant manager Pep Lijnders defended him in the pre-match press conference.
He said: "Darwin is full of desire.
"You see that in each game, and if we would only judge players on the goals, that would be so unfair.
"I feel that there is a good connection between Mo [Salah] and Darwin, for example - the way they see each other, they assist each other.
"And, I feel above everything, that Darwin is playing a much better season than last year - the way how he defends for the team, the way how he controls the centre and at the same time puts the press on, the way he goes, the way how he chases back."
52 minutes agoBy Jack Cunningham
Big chance for Elliott
Harvey Elliott has impressed from off the bench in recent weeks, and tonight, he gets a proper chance from the start.
Can he take it?
59 minutes agoBy Jack Cunningham
Liverpool vs West Ham: Pre-match facts
This is the first League Cup meeting between Liverpool and West Ham since the fourth round in 1988-89, with the Hammers winning 4-1 at Upton Park under John Lyall.
West Ham have won just one of their last 55 away games against Liverpool in all competitions (D14 L40), beating them 3-0 in the Premier League in August 2015.
Liverpool have won five of their last six League Cup quarter-final ties, with the exception being a 5-0 loss to Aston Villa in 2019-20 when most of the their first team were away at the Club World Cup.
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