Manchester United will face Manchester City in the Carabao Cup semi-finals, with Leicester City taking on Aston Villa in the other tie.
City made their way to the last four by beating Oxford United on Wednesday night as Raheem Sterling scored twice at the Kassam Stadium.
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They will face local rivals United who also beat lower-league opposition in the quarter-finals. United were victorious against League Two side Colchester United.
On drawing rivals City in the last four, United boss Ole Gunnar Solskjaer told Sky Sports: "We always want to win trophies and we want to win games.
"We've got a nice little draw coming up so it'll be exciting times coming up. I don't think anything is written in the stars. We just work hard and you take what you get and you do the best out of it. We've shown before we can do well against City."
The other semi-final will see the Premier League's second-placed side Leicester face Dean Smith's Aston Villa in their bid to play either Manchester side in the final.
The Foxes beat fellow Premier League side Everton on penalties to reach the semis, whilst Villa comfortably dispatched Liverpool's youngsters on Tuesday night.
The semi-final first legs are scheduled to take place in the week commencing January 6, with the return legs set for the week commencing January 27.
The final will take place at Wembley on Sunday March 1, 2020.
Quarter-final reports and highlights
Marcus Rashford had a hand in all three goals as Manchester United beat Colchester 3-0 to reach the Carabao Cup semi-finals.
Raheem Sterling's double sent Manchester City into the Carabao Cup semi-finals as they beat Oxford Utd 3-1 on Wednesday.
Leicester squeezed through to the Carabao Cup semi-finals with a 4-2 penalty shootout win over Everton after the Toffees fought back from 2-0 down.
Aston Villa eased into the semi-finals of the Carabao Cup after beating the youngest side in Liverpool's history 5-0 on Tuesday night.
The semi-final stats
- Leicester have reached the League Cup semi-final for the first time since the 1999/2000 season, when they went on to win the trophy.
- Manchester United have reached their 15th League Cup semi-final - only Liverpool have reached more in the competition's history (17).
- Manchester City are currently unbeaten in 15 League Cup matches (W11 D4), the longest unbeaten run in this competition since Chelsea went 18 games without defeat between 2004 and 2008 - though Chelsea were eliminated via penalties during that run.
- Aston Villa have reached the semi-finals of the League Cup for the first time since the 2012/13 campaign, while Liverpool have been eliminated at the quarter-final stage of the competition for the first time since 2007/08.