After knocking out Manchester City and Manchester United in the last two rounds, Newcastle United will travel to Chelsea for a place in the semi-finals.
The Magpies defeated Manchester United 3-0 at Old Trafford on Wednesday.
Chelsea booked a place in the last eight with a 2-0 win over Championship side Blackburn Rovers at Stamford Bridge on Wednesday.
West Ham United face a difficult trip to Anfield to face Liverpool, who won 2-1 at Bournemouth.
The Hammers dispatched Arsenal 3-1 in the fourth round tie.
Another all-Premier League tie in the quarterfinals sees Everton host Fulham while League One side Port Vale will play at home to Middlesbrough.
The quarter-finals will take place in the week commencing December 18.
Carabao Cup quarter-finals draw:
Everton v Fulham
Chelsea v Newcastle
Port Vale v Middlesbrough
Liverpool v West Ham
