The 50-year-old, who took over at Inter in November, spent four years at the Etihad and led City to the Premier League title in 2012, with Toure playing a key part for his table-topping side.
The former Barcelona midfielder was integral again as City won the domestic crown last season under Mancini's successor Manuel Pellegrini, but he has been persistently linked with various clubs since the summer.
When Mancini, who took over at Inter in November, was asked about his plans for the next transfer window on Gazzetta TV's Senza Appello talkshow - which can be viewed on the club's official website www.inter.it - he suggested Toure may be open to the idea of a move
"I'm sure we'll do some good business," he said
"Yaya Toure? He's played in almost every league, except for Germany and Italy
If, as seems to be the case, he wants to try Serie A we'll look into the possibility, but it won't be easy
"He's a player with incredible technical ability
I've not come across many like him."
Toure, who began his career at Belgian side Beveren, also played for Metalurh Donetsk, Olympiacos and Monaco before joining Barcelona in 2007.
That heralded a trophy-laden run in his career as he won two Primera Division titles, the Champions League, UEFA Super Cup, World Club Cup and the Copa del Rey in just three years with the Spanish giants.
The 31-year-old has so far added two domestic titles, an FA Cup and a League Cup to his medals haul since joining City in 2010.
Source : PA
Source: PA