United and Liverpool overcame London giants Chelsea and Arsenal respectively in two remarkable last-16 ties on Wednesday evening.
The Reds downed the Gunners 5-4 on penalties after a 10-goal thriller over 90-minutes at Anfield in which Divock Origi scored a last-minute equaliser for the hosts.
Marcus Rashford was the hero for Ole Gunnar Solskjaer's men with a thunderous 35-yard free-kick to settle the tie in a 2-1 victory after Michy Batshuayi initially cancelled out the England striker's first-half penalty.
Colchester, currently in the third-tier of English football, will face five-time winners United after they reached the last eight for the second time in their history.
League One side Oxford United have been rewarded for their penalty shoot-out triumph over Sunderland with a home tie against champions City while Liverpool travel to Aston Villa.
The final tie pits another all-Premier League clash between Everton and Brendon Rodgers' high-flying Leicester City.
Oxford United v Manchester City
Manchester United v Colchester United
Aston Villa v Liverpool
Everton v Leicester City