There is a feeling internally that the team needs an older head to help guide them towards trophy-winning moments, and it is something they have looked at closely this summer.
The desire for new leadership became apparent when Chelsea attempted to sign 33-year-old Granit Xhaka from Sunderland.
Xhaka is a player Xabi Alonso knows and trusts, and would have brought a new layer of quality to the dressing room and the pitch. Similarly, Chelsea view Stones as a player who can elevate their potential for next season.
Stones is available on a free transfer following the expiry of his Manchester City contract, but since the end of last season he has been focused on World Cup duties with England.
Options are now being explored by the 32-year-old centre-back, both in England and abroad.
Chelsea are putting themselves firmly in the frame to sign him, while Arsenal are another English side to have contemplated the idea. Stones has a good relationship with Mikel Arteta, which might give the Gunners an edge, while Everton have been very keen on the idea of signing him as well.
Stones has also attracted attention from Italian sides Inter Milan and Juventus as top next destinations to continue his career.
Stones won the Premier League six times with Manchester City and also has experience of winning the Champions League.
Chelsea feel such experience could help change the mindset of their squad as they push for growth in the 2026/27 season, but they are waiting to discover if they can truly win the race to sign him.
Chelsea are already in talks to sign Maxence Lacroix from Crystal Palace in a bid to improve their defence - and Stones would be signed additionally if they can put together an offer that tempts him.
It is obvious that Stones and Lacroix, 26, are at opposite stages of their career and that would change the dynamic of the squad at a time when they are looking to offload players.
Benoit Badiashile, Trevoh Chalobah, Tosin Adarabioyo, and Axel Disasi are among those who could be moved on.