The Reds, who have won the League Cup a record nine times, will be aiming to make the final four of the competition, buoyed by early exits for the likes of Tottenham, Manchester United, Manchester City and Arsenal.
As a result, Liverpool will be favourites to win the trophy for only the second time since Jurgen Klopp arrived at Anfield, the German guiding them to the cup in 2021/22.
West Ham will be no pushovers though having knocked out Arsenal already. The Irons, who won the Europa Conference League last season, will be aiming to get their hands on the Carabao Cup for the first time.
Here is how you can tune in to the Reds' next game on TV.
HOW TO WATCH LIVERPOOL VS WEST HAM ON TV
Bar the 4-3 victory over Fulham, all of Liverpool's December fixtures have been broadcast on TV in the United Kingdom. Wednesday's quarter-final is no different.
The Reds will be live on Sky Sports for the 20:00 (GMT) kick-off against West Ham, while the game will also be available on BBC Radio 5 Live if you're on the move.
DAZN are the rights holders for Canada, while they will also be showing the game in large parts of Europe, including Spain, Italy and Germany.
For those in the United States and the Caribbean, the game will be broadcast on ESPN+, with the majority of South America being able to see the action on Star+.
In Australia and a host of Asian countries, beIN Sports will be showing the match, while SuperSport are the main rights holders across Africa.
Of course, match highlights will be available after the full-time whistle on LFCTV, while you can keep up to date with the action on the Anfield Watch socials.