Holders Manchester City will travel to Arsenal in the standout tie of the Carabao Cup quarter-final draw.
Joint Premier League leaders Everton welcome Manchester United to Goodison Park, while Tottenham are away to Championship side Stoke City.
Meanwhile, Brentford's reward for beating Fulham is a home tie against Newcastle United in the club's first ever League Cup quarter-final.
All quarter-final ties are to be played the week commencing 21 December 2020.
Arsenal progressed in a penalty shootout against Liverpool following a goalless draw in the final tie of the fourth round on Thursday.
The meeting at Emirates Stadium with Pep Guardiola's Manchester City, who eased to a 3-0 win over Burnley, will see manager Mikel Arteta face his former club in a repeat of last season's FA Cup semi-final, which Arsenal won 2-0 on their way to winning the trophy.
READ ALSO:Â 2020/21 Champions League draw: Messi faces Ronaldo as Man United play PSG
In-form Everton thrashed West Ham 4-1 to reach the last-eight and their upcoming opponents Manchester United claimed a 3-0 win over Brighton.
Stoke City defeated last season's runners-up Aston Villa 1-0 on Thursday to set up their tie against Jose Mourinho's Spurs, who overcame Chelsea on penalties.
Last season's beaten Championship play-off finalists Brentford exacted revenge for that defeat on promoted Fulham with a 3-0 victory to record their best ever League Cup showing, with Steve Bruce's Newcastle lying in wait after they edged past League Two Newport County on penalties.
The semi-final ties are then scheduled for 5 and 6 January 2021, with the final of the 2020-21 EFL Cup taking place on 28 February 2021 at Wembley.
The winners of this season's tournament will not qualify for the Europa League as in the past, but will instead go into the Uefa Europa Conference League, a new European competition.
Quarter final draw
Stoke City v Tottenham
Brentford v Newcastle United
Arsenal v Manchester City
Everton v Manchester United