Champions Manchester City will face Manchester United at Old Trafford in the Carabao Cup semi-final.
Championship side Brentford, the lowest ranked club left in the competition, are away to Tottenham in the other semi-final.
The ties are single-leg matches instead of the traditional two-legged format in order to ease fixture congestion caused by the delayed start to the season.
They will be played on the week commencing 4 January 2021.
United progressed after late goals from Edinson Cavani and Anthony Martial gave them a 2-0 win at Everton in the fourth and final quarter-final tie on Wednesday.
City, 4-1 winners at Arsenal on Tuesday, are looking to win the competition for the fourth successive season. They beat United 3-2 on aggregate in last season’s two-legged semi-final.
Tottenham won 3-1 at Stoke City on Wednesday to advance with Gareth Bale, Ben Davies and Harry Kane among the goals. Their meeting with Brentford, who beat Newcastle United 1-0 on Tuesday, will be the first between the teams since 2000.
Tottenham boss Jose Mourinho is a four-time winner of the competition but Spurs have not won a major trophy since 2008.
The final of the 2020-21 EFL Cup has been rescheduled to 25 April 2021 at Wembley having originally been due to take place on 28 February. It has been put back in an attempt to have as many supporters in attendance as possible.
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.
Semi Final Draw
Manchester United v Manchester City
Tottenham v Brentford