The 32-year-old centre-back is available without a transfer fee after leaving City when his contract expired at the end of June, making him one of the highest-profile free agents on the market.
Inter Milan are also monitoring the situation as they consider a potential approach for the defender.
Chelsea's recruitment plans extend beyond Stones. The Blues remain in negotiations over a deal for Crystal Palace defender Maxence Lacroix and are also evaluating Como's Jacobo Ramon as they explore further reinforcements at the back.
To accommodate potential arrivals, Chelsea are aiming to reduce the number of central defenders in their squad. Trevoh Chalobah is in discussions over a move to Como, while Axel Disasi and Benoit Badiashile have both been made available for transfer.
Stones would arrive with an outstanding list of honours following an eight-year spell at Manchester City. Signed from Everton for 47.5 million pounds in 2016, he featured 295 times for the club, collecting six Premier League crowns, the Champions League, two FA Cups, five League Cups, three Community Shields, the Club World Cup and the UEFA Super Cup.
Before spells with Everton and City, he began his senior career at Barnsley. Internationally, Stones has won 93 England caps and was part of the squad that secured a third-place finish at the World Cup.
Morgan Rogers has completed a British record £117 million move from Aston Villa to Chelsea, ending months of speculation after signing a six-year contract with the option of a further season.
Marcus Rashford is set to rejoin Manchester United for their pre-season preparations as uncertainty continues over his long-term future at Old Trafford.
Pep Guardiola has reportedly emerged as a potential candidate to become Italy's next national team coach after holding talks with new Italian Football Federation (FIGC) technical director Paolo Maldini.
Two-time Ballon d'Or winner and England, Liverpool and Newcastle great Kevin Keegan has died at the age of 75 following a battle with stage four cancer.
