Last season's runners-up Newcastle play at Chelsea in the Carabao Cup quarter-finals, while Liverpool face West Ham.
Newcastle have eliminated Manchester City and Manchester United in the past two rounds and travel to Stamford Bridge for the next round.
Everton entertain Fulham in an all-Premier League tie and League One outfit Port Vale play at home against Middlesbrough of the Championship.
Matches will be played in the week commencing 18 December, 2023.
On Tuesday, Port Vale moved into the quarter-finals for the first time in their history with a 1-0 win at League Two Mansfield Town, while Middlesbrough came from behind to defeat Exeter City 3-2.
Newcastle beat last season's winners Manchester United 3-0 in a rematch of the 2022-23 final, with West Ham also scoring three times in their 3-1 victory against an Arsenal side that are second in the Premier League.
Liverpool won 2-1 at Bournemouth, Everton easily defeated fellow Premier League side Burnley 3-1, Chelsea beat Championship outfit Blackburn Rovers 2-0 and Fulham also won against second-tier opposition, 3-1 away at Ipswich Town.
Only three of the remaining eight teams - Chelsea, Liverpool and Middlesbrough - have won this trophy, with Everton, Newcastle and West Ham each losing in the final on two occasions apiece.
Carabao Cup quarter-finals
Everton v Fulham
Chelsea v Newcastle
Port Vale v Middlesbrough
Liverpool v West Ham
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