Mourinho welcomed the tough draw, which was made minutes after his side beat Stoke 1-0 at Stamford Bridge to reach the last 16.
Another highlight of the fifth round will be the Emirates Stadium tussle involving Arsenal and Liverpool, two teams who remain in with a shot at the league and FA Cup double.
Big-spending City are chasing a quadruple, having already reached the Capital One Cup final, where Sunderland await them. And while Mourinho recognises City's obvious quality, and goal threat at the Etihad Stadium which will stage their FA Cup encounter, the Portuguese boss has told his team to embrace the challenge.
Oscar's free-kick ensured Mourinho could celebrate his 51st birthday in style at Stoke's expense, and Chelsea will be able to prepare for the cup tie when when face City in Manchester on February 3, almost a fortnight before the cup match.
Mourinho said: "Our priority for the season is to improve and the best way to improve is difficult tests.
"We play against the best team twice in 15 days, in the best stadium, in the stadium where they win every week, smash everyone, score four, five goals every game even against the big teams like Arsenal, Tottenham, (Manchester) United.
"It's a good thing for us. We are playing very well in my opinion. It's good for us. If we lose, we lose against the best. If we don't lose, it's fantastic."
And, perhaps in a first round of mind games ahead of what will be a mouthwatering double-header, Mourinho added: "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."
The FA Cup ties will be played on the weekend of February 15 and 16, days before the Champions League last-16 games which pit Arsenal against Bayern Munich and City against Barcelona.
Ten-time cup 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.
Holders Wigan produced arguably the shock of the fourth round by beating Crystal Palace 2-1 and next face Ole Gunnar Solskjaer's Cardiff.
The two lowest-ranking teams remaining in the competition, Sheffield United and Preston of League One, could vie for a place 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 on Sunday 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.