The two remaining non-Premier League teams will play against each other in the two other ties, which were drawn on Wednesday. Everton will visit Fulham, while Championship Middlesbrough will host League One surprise package Port Vale.
Newcastle defeated the defending champions 3-0 at Old Trafford on Wednesday, and following their much-needed victory over Blackburn Rovers, they will now face a faltering Chelsea team.
West Ham should be pumped going into their match at Anfield after easily defeating Arsenal 3-1 at the London Stadium.
Out of the eight teams left, only three have ever won the League Cup: Liverpool, Chelsea, who have won five times, and Middlesbrough, who won it in 2004.
Following their 1-0 victory over League Two Mansfield Town on Tuesday, Port Vale advanced to the quarterfinals for the first time in their history.
The week of December 18 will see the quarterfinal matches.
Carabao Cup Quarterfinal Draw
Everton vs. Fulham
Chelsea vs. Newcastle
Port Vale vs. Middlesbrough
Liverpool vs. West Ham