Stones, 32, ended a decade-long spell at the Etihad when his contract expired on 30 June, a stay that yielded six Premier League titles, three FA Cups, three League Cups and the 2023 Champions League.
Arsenal, Chelsea, Inter Milan and his former club Everton have all been credited with interest in the versatile centre-back following his performances for England at this summer's World Cup, but according to Gianluca Di Marzio, Juventus are the only club to have made concrete contact with his camp so far, with talks understood to have progressed to discussions over personal terms.
Juventus are looking to strengthen their defence after a disappointing campaign in which they finished sixth in Serie A and missed out on Champions League qualification, the competition they have won twice before but will sit out again this coming season in favour of the Europa League.
Signing Stones on a free transfer would allow Luciano Spalletti's side to add proven experience without committing to a transfer fee, though his wage demands and recent injury history remain factors under consideration at Juventus and elsewhere.
Were the move to go through, Stones would join a defensive unit already including Bremer, Pierre Kalulu, Lloyd Kelly and Daniele Rugani, though question marks remain over the futures of Bremer and Kelly as Juventus continue reshaping their backline this summer. Stones made just nine Premier League starts in his final season at City amid recurring fitness issues, leaving Juventus to weigh his pedigree against the number of matches he can realistically be expected to play.
Fabrizio Romano reported earlier in the window that Stones had also been offered to Inter Milan and Milan, though neither club has advanced their interest to concrete talks, with Romano citing wage expectations and Stones's injury record as obstacles.
Stones was capped five times for England during their run to this summer's World Cup, remaining one of the more decorated free agents on the market this summer regardless of which club he eventually joins.