Stones has already left Manchester City as a free agent after his contract expired at the end of June with Bernardo Silva moving on to Real Madrid after his own deal ran out in Manchester.
The 32-year-old won six Premier League titles as a key part of Pep Guardiola's defence at the Etihad Stadium, but the latter's own exit from the club has triggered several squad departures, including Nathan Ake and Manuel Akanji leaving as Enzo Maresca returns.
Stones remains keen on a new challenge, having never played outside England before, and Juventus can offer him UEFA Europa League football if he accepts a move to Turin.
Reports from Sky Sports Italia claim the club have already reached out to Stones' representatives over a possible two-year contract, but nothing will be confirmed until he's finished with England duty in the USA.
Stones started England's World Cup opening win over Croatia, but he's remained on the bench since, with knockout stage cameos against DR Congo and Mexico.
His performances to get England over the line to victory in both games has caught Juve's eye with the Italian club confident his experience could be vital to their cause next season.