The former Juventus player has been told by new Real boss Bernd Schuster that he no longer has a future at the Bernabeu, prompting interest from several of Europe's top sides.
And Mancini, who is a big fan of the Brazilian, would consider ending the 31-year-old's Spanish nightmare.
"Great players are always welcome at a team which is already very strong and that can improve," Mancini said.
"We will see in the coming days but Emerson is a great player, one of the best in the world in his position."
Emerson, who also has Serie A experience with Roma, made just 16 appearances for Real since he followed coach Fabio Capello Real from Juventus at the beginning of last season.
Meanwhile, there is a chance Inter could revive their bid for Roma defender Cristian Chivu. When questioned on the subject of the Romanian's transfer to the Giuseppe Meazza, Mancini said: "I don't know, we will see what happens. I honestly don't know."