The Argentina international has also been interesting Liverpool.
Mancini's agent, Giorgio De Giorgis, spoke about City's pursuit of Lavezzi and even claimed England midfielder Gareth Barry could be a makeweight in the transfer.
He told Radio CRC: "Manchester City's interest in Lavezzi could be a reality.
"But 31million euros for Lavezzi, I think it's excessive.
"However, to find a player who is ready like Pocho is, it's not easy.
"The only one could be (Gareth) Barry, who is an England international and does not have a high salary."
Lavezzi is under contract with Napoli until June 2015 and has a release clause of £26.8m.