Mancini admires De Rossi, but says a move for the Italy World Cup winner is unlikely to go ahead.
"In January we have a big problem because we lose Yaya and Kolo," said Mancini.
"I hope we don't lose any more players through injury. We need to sell two or three players and then we'll see what can happen.
"I don't think we will get De Rossi because he was born in Rome and it's unlikely he'll leave the city.
"I asked the owner for [Lionel] Messi but it's not possible!"