Roberto Mancini’s City make the trip to Stamford Bridge in the Premier League on 27 February and will return seven days later if they beat Stoke City in their fifth round replay next Wednesday night.
The tie also pairs John Terry with England colleague Wayne Bridge after the Blues skipper was accused of having an affair with his ex-girlfriend.
Tottenham will visit Fulham if they can beat Bolton in a replay.
FA CUP | QUARTER-FINAL DRAW
Chelsea v Man City or Stoke City
Fulham v Bolton or Tottenham
Reading/W Brom v C Palace/A Villa
Portsmouth v Birmingham