The 32-year-old left City this summer following the expiry of his contract this month, and has attracted interest from a number of Serie A clubs, with Inter the latest to join that list.
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Inter have been exploring the conditions of a potential deal with Stones, and have added him to a list of potential defensive recruitments, per Sky Sports.
They will have to fend off Italian rivals Juventus for the defender's signature this summer.
The reigning Italian champions will look to bring in Stones to join his former teammate Manuel Akanji in defence ahead of the new Serie A season.
Stones will assess his options following this summer's World Cup with England, and it looks like Italy will be the chosen destination.