The Carabao Cup semi-finals will play host to a Manchester Derby tie.
Manchester United eventually saw off Colchester 3-0 in their quarter-final, while Manchester City saw off Oxford United 3-1.
Man United were unable to break down Colchester in the first-half.
But after Marcus Rashford broke the deadlock on 51 minutes, Ole Gunnar Solskjaer's side were out of sight within the 10 minutes that followed.
Ryan Jackson's own goal and Anthony Martial's finish put them 3-0 up with half an hour to go.
Joao Cancelo gave City the lead on 22 minutes at Oxford. Matty Taylor equalised for their League 1 opponents.
But Raheem Sterling's two close-range goals made sure Pep Guardiola's side progressed.
Repeat of recent fixtures
In the third quarter-final, Leicester City beat Everton on penalties to join United, City and Aston Villa in the last-four.
James Maddison and Jonny Evans had put the Foxes in front, before Everton took the game to extra-time with goals from Tom Davies and Leighton Baines.
Kasper Schmeichel made two saves in the ensuing penalty shootout as Leicester prevailed 4-2.
Leicester will take on Villa, who they thrashed recently in the Premier League. And United will hope to repeat their Manchester Derby win when they face City over two legs in January.