Instead, The Special One has claimed that all the pressure will be on Manuel Pellegrini's men.
Two of the Premier League's big guns were drawn together in the fifth round of the cup immediately after Mourinho's side had beaten Stoke 1-0 on Sunday.
Oscar's free-kick ensured Mourinho could celebrate his 51st birthday in style, and he refused to have the smile taken off his face by a trip to the Etihad in the next round.
When asked if he had seen his birthday happiness taken away, he asked: "Taken away what?"
City have scored 110 goals in all competitions this season and have put numerous teams to the sword on their own turf.
Arsenal and Tottenham were hit for six while Manchester United conceded four on the blue half of the city.
Chelsea are already slated to head there in the league on February 3 and will now return over the weekend of February 15 and 16.
"It's good, that's good," 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, 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 insisted there will be no pressure on his side in those matches.
"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," he added.
"They feel now the same thing I was feeling here (at Chelsea) in 2004, 5, 6, 7. They have the best team and have to win and if we (Chelsea in the past) don't it's because we do something wrong and they must feel the same."
The Chelsea-City match-up was not the only blockbuster in the draw, with Arsenal and Liverpool also drawn together.
To add further excitement, the fixtures will be booked in for the weekend before the Champions League last-16 games, which pit Arsenal against Bayern Munich, Chelsea against Galatasaray 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 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 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.