Having managed to avoid each other in the competition’s opening rounds, the top flight’s four leading clubs will now come together in the last 16 on the weekend of February 15-16.
Chelsea’s trip to the Etihad Stadium will follow hot on the heels of their away game at City a week on Monday, but the London club’s manager Jose Mourinho took the draw in his stride.
“No problem. If you want to be the best, you have to play against the best,” he told ITV after his side’s 1-0 success at home to Stoke City in the fourth round on Sunday.
“So it’s good for us — good experience, good game, big game, good.”
Chelsea and City are considered the biggest challengers to current league leaders Arsenal, but Mourinho suggested that Manuel Pellegrini’s side would approach the tie as favourites.
“One team is an ended product, the other team is a team that needs to improve and has a long way to go,” he said.
Arsenal beat Liverpool 2-0 when the sides last met in November and the teams are due to face off again at Anfield in the league a week before their encounter in the cup at the Emirates Stadium.
There were two other all-Premier League ties in the draw, with League Cup finalists Sunderland drawn to face Southampton and Everton manager Roberto Martinez handed a tie against his former club Swansea City.
Holders Wigan Athletic, meanwhile, will visit Cardiff City after eliminating Crystal Palace on Saturday.
Draw for the fifth round of the English FA Cup, made at Wembley Stadium on Sunday (ties to be played the weekend of February 15-16):
Manchester City v Chelsea
Sheffield United or Fulham v Nottingham Forest or Preston North End
Arsenal v Liverpool
Brighton and Hove Albion v Hull City
Cardiff City v Wigan Athletic
Sheffield Wednesday v Charlton Athletic
Sunderland v Southampton
Everton v Swansea City