The former City manager brought Toure to the Premier League ahead of his first full season in charge at the Etihad, signing the Ivorian for £24m from Barcelona in 2010.
Inter have been linked with a move for Lucas Leiva, but with Liverpool reluctant to sell Mancini may now turn his attention to an ambitious summer move for Toure.
Mancini said: “I bought Yaya five years ago. It was really difficult to take him there. He is a fantastic player and in the future, if he wants to change, and to try and play in Italy, Inter is open for him.
“It depends because he is a City player in this moment.”
“Yaya is one of the strongest players in the world,” Mancini was earlier quoted as saying by Italian newspaper Il Giornale. “He still is.
“He has played in so many teams. He has been in leagues in Belgium… Spain and England. Italy is the one missing. This could be the right opportunity for him to come and try.
“We are building a team. There are players that change the look of a team, and Yaya is one of them.
“Next year we could try. We need to bring three champions, and we will see that we will be ready to fight for the Scudetto.”
Toure, who is currently on international duty at the Africa Cup of Nations, is under contract with the City for the next two-and-a-half seasons.
The 31-year-old has scored seven goals in 18 Barclays Premier League appearances for Manuel Pellegrini’s side this term.
Inter are currently 10th in Serie A, 23 points adrift of leaders Juventus.