Leicester and Aston Villa will go up against each other in an equally anticipated Midlands derby, with the ties to be played over two legs in the weeks commencing 6 and 27 January.
Manchester United and Leicester will be at home in their first legs.
Pep Guardiola’s Manchester City have won the tournament in each of the last two seasons and four times in the last six years.
Manchester City beat League One Oxford United 3-1 on Wednesday, while Manchester United overcame League Two Colchester United 3-0 at Old Trafford.
Leicester City, who won the competition in 1999-2000, beat Everton 4-2 on penalties after a 2-2 draw at Goodison Park.
Aston Villa, who reached the semi-finals for the first time since 2012-13, beat a youthful Liverpool 5-0 on Tuesday.
Manchester City were beaten 2-1 by Ole Gunnar Solskjaer’s Manchester United in the Premier League on 7 December.
The two sides last met in the competition at the fourth round stage in 2016 with United winning 1-0.They last met at this stage in 2010 with United winning 4-3 on aggregate.