At 32, Stones, who represented England at the World Cup, is available without a transfer fee after he departed City this summer at the end of his contract.
Stones made 295 appearances for City after joining from Everton for £47.5m in 2016 and has won every trophy possible with the side who were managed by the legendary manager Pep Guardiola.
The veteran defender helped the club win six Premier League titles, the Champions League, two FA Cups, five League Cups, three Community Shields, the Club World Cup and the Uefa Super Cup.
Now, as per Fabrizio Romano, Stones is set to decide between Italian giants Juventus and Inter Milan who are close to agreeing terms with him this week.
“Understand Inter are set to discuss a two year deal with John Stones as a free agent, talks ongoing.
“Juventus also approached his camp over the weekend.
“Decision up to the English CB who also has proposals in Premier League.”
Chelsea, who were close to bringing Stones in, look set to land Maxence Lacroix from Crystal Palace which is a huge boost for both Italian clubs who are now in a two horse race for the defender.
Stones only managed 18 appearances across all competitions this past season due to a persistent injury, something Inter and Juventus may still be cautious of as they continue negotiations.