The two Manchester clubs face lower league opposition with two all-Premier League ties completing the last eight of the competition.
Manchester United will face League Two outfit Colchester United in the Carabao Cup quarter-finals while Liverpool travel to Aston Villa.
Holders Manchester City are away at Oxford United, with Everton hosting Leicester City.
Colchester are the lowest ranked team left in the competition having beaten fellow League Two side Crawley Town on Tuesday to reach this stage for just the second time in their history.
John McGreal’s side have already caused a shock this season after beating Tottenham on penalties in Round Three last month.
Former England goalkeeper David James, who helped conduct the draw, said: “If they (Colchester) are going to enjoy a cup trip, that’s the place they want to go to get an amazing result. Playing at Old Trafford, it’s a magical draw.”
Liverpool, who have won the Carabao Cup a record eight times, beat Arsenal on penalties on Wednesday after a thrilling 5-5 draw at Anfield.
However, their participation in the competition could be in doubt after manager Jurgen Klopp admitted the club may have to forfeit their quarter-final due to fixture congestion.
The fixtures are due to be played the week commencing December 16, but Liverpool will be unable to participate as they head to Qatar for their Club World Cup semi-final on December 18.
The EFL say they are in discussions with the Merseyside club over an alternative date.
Oxford United, winners of the trophy in 1986, have been handed a plumb home tie against holders Manchester City.
Karl Robinson’s side beat fellow League One outfit Sunderland on penalties to reach this stage for the first time since 1987-88.
Manchester City have a formidable recent record in the competition. They have lifted the trophy four times in the last six seasons, including the last two, and have not lost a cup tie since October 2016.
Another all-Premier League tie completes the draw, with Everton hosting Brendan Rodgers’ Leicester at Goodison Park.
The Toffees beat Watford 2-0 at on Tuesday to reach the quarter-finals for just the third time in 31 years.
Leicester, meanwhile, are three-time winners of the competition, most recently in 2000, and won 3-1 at League One side Burton Albion to reach this stage.
Carabao Cup quarter-final draw in full
Oxford United v Manchester City
Manchester United v Colchester United
Aston Villa v Liverpool
Everton v Leicester City
