Toure was signed by Mancini during the Italian's stint at the Etihad Stadium from 2009 to 2013.
The Ivory Coast international is under contract until 2017, but there has been speculation over a potential move to pastures new, with Inter and Paris Saint-Germain mooted as possible destinations.
"Yaya's played in all the top leagues apart from Germany and Italy and if he, as it seems, would like to come to Italy, then there is this possibility," Mancini told GazzettaTV.
"It's not going to be easy. He's a player with personality and incredible technical quality, but if he were to come to Italy, then Inter would certainly be his first choice.
"Let's first just see what happens with Financial Fair Play. I'm convinced that we'll sign some good players who will boost the quality of the side. Yes, [I've been given carte blanche to spend], but they forgot to give me the pen."
Speaking about the chances of Inter - who sit ninth in Serie A - winning the league next season, Mancini added: "Of course we can.
"I'm so confident because of what we are doing. The foundations are solid. I can see the lads improving all the time; everybody's getting better.
"Next season, we are aiming to fight it out with Juve, Napoli and Roma."
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