City must beat Real Madrid at Eastlands on Wednesday and Borussia Dortmund in their final game to keep alive their slim hopes of qualifying for the knockout stage.
Mancini rates Ronaldo higher than current World and European Player of the Year Lionel Messi and outlined the scale of the task facing City's players in handling the former Manchester United star.
"We'll call the police! He's a top player and he deserves to win the Ballon D'Or. He scored so many goals last year and that helped them to finish above Barcelona," the Daily Mirror quoted Mancini, as saying.
"I hope he can have a bad night on Wednesday. When you come up against a player ho can score one or two goals every game it is difficult. If they leave Cristiano at home, it's better," he added.
According to the report, Wednesday night's game will be the first time Ronaldo has played in Manchester since his world record 80 million pound move from United to Real in 2009.
And Mancini admitted the 27-year-old former World Player of the Year will be fired up for the encounter against United's local rivals.
"For him it will be [important] yes, but also for them [Real] it's an important game. They still have a chance of going through to the second stage. And for Ronaldo, he's coming back to Manchester," he said. (ANI )