Chelsea secured another home draw for the Carabao Cup quarter-finals, although Newcastle await in the next round.
The Magpies demolished Manchester United in the fourth round on Wednesday as they target going one better than their defeat in last year's final, while Chelsea beat Blackburn.
West Ham's reward for downing Arsenal at London Stadium is a visit to Liverpool, who beat Bournemouth courtesy of a fine Darwin Nunez goal.
League One side Port Vale take on Middlesbrough of the Championship on their first appearance at this stage of the competition. That tie ensures there will be one non-Premier League team in the semi-finals.
Everton will host Fulham after beating Burnley on Wednesday night, while the Cottagers overcame Ipswich away from home.
The ties will be played on the week commencing Monday, December 18.
Carabao Cup draw in full
Everton vs Fulham
Chelsea vs Newcastle
Port Vale vs Middlesbrough
Liverpool vs West Ham
