Manuel Pellegrini's City, winners in 2011 and runners-up to Wigan last year, recovered from two goals down to beat Watford 4-2 in the fourth round on Saturday and meet Chelsea following the Blues' slender 1-0 victory over Stoke.
Ten-time winners Arsenal are currently out in front in the Premier League and tackle Brendan Rodgers' ambitious Liverpool after the top-flight sides ousted Coventry and Bournemouth respectively.
Upon hearing his Chelsea side had been drawn against domestic title rivals City, manager Jose Mourinho told ITV: "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."
Holders Wigan produced the shock of the fourth round by beating Crystal Palace 2-1 and now face Ole Gunnar Solskjaer's Cardiff in a match set to take place on the weekend of February 15-16.
The two lowest-ranking teams remaining in the competition, Sheffield United and Preston of Sky Bet League 1, could face each other in the quarter-finals if they can get through respective replays against Fulham and Nottingham Forest.
The Blades held Fulham to a 1-1 draw and go to Craven Cottage on February 4 while Preston invite Nottingham Forest to Deepdale for a decider following Friday night's stalemate.
Two remaining all-Premier League clashes will see Sunderland - fourth-round victors over non-league Kidderminster - entertain Southampton and 1995 winners Everton tackle Swansea at Goodison Park.
Hull's victory over Southend earned them a return trip south, this time to Brighton, while two Championship sides will go head-to-head at Hillsborough when Sheffield Wednesday host Charlton.
Fifth round draw
Manchester City v Chelsea
Sheffield United/Fulham v Nottingham Forest/Preston
Arsenal v Liverpool
Brighton v Hull
Cardiff v Wigan
Sheffield Wednesday v Charlton
Sunderland v Southampton
Everton v Swansea
Matches to be played on the weekend of February 15-16.