Manuel Pellegrini's City, winners in 2011 and runners-up to Wigan last year, beat Watford in the fourth round on Saturday, while Chelsea booked their passage with a 1-0 victory over Stoke on Sunday, Oscar's first-half free-kick proving decisive.
Chelsea manager Jose Mourinho said: "No problem. If you want to be the best you have to play against the best, so it's good for us. Good experience, good game, big game.
"We are ready to go there and enjoy. We are going to go there with a good attitude. We have nothing to lose, they have everything to lose, they are the team that was made to win."
Ten-time winners - and current Premier League pacesetters - Arsenal were paired with Liverpool after their victories over Coventry and Bournemouth respectively.
There are four all-Premier League ties in total as Everton were drawn against Swansea - one of manager Roberto Martinez' former clubs - while Sunderland will host Southampton.
Holders Wigan play Cardiff while the two lowest-ranking teams, Sheffield United and Preston, could face each other in the quarter-finals if they prevail in replays against Fulham and Nottingham Forest.
Hull's victory over Southend earned them a trip to Brighton, while two Championship sides will meet at Hillsborough where Sheffield Wednesday host Charlton.
Manchester City v Chelsea
Fulham/Sheffield Utd v Nottingham Forest/Preston
Arsenal v Liverpool
Brighton v Hull City
Cardiff City v Wigan Athletic
Sheffield Wednesday v Charlton
Sunderland v Southampton
Everton v Swansea City
Ties will be played on the weekend of February 15-16