De Rossi has been touted as a potential City purchase for some time.
With Mancini concerned about his options when Yaya Toure departs for the African Nations Cup next month, there had been suggestions City would make a move for the 27-year-old Roma man, who came on as a substitute in Italy's World Cup final triumph over France in 2006.
However, while Mancini concedes he may need to bring in reinforcements, he doubts whether De Rossi can be prised away from the Italian capital.
"I don't think so," he said. "De Rossi was born in Rome and it's unlikely that he'll leave the city.
"There are players that could be good for us. But every time we want to buy a player their clubs ask for lots of money."