The England international has developed into one of Europe's most celebrated ball-playing defenders under Pep Guardiola, thriving in an inverted right-back role over the past couple of years.
Often linking arms with Rodri in the middle of Guardiola's 3-2-4-1 system, Stones made 34 appearances during the Citizens' treble-winning 2022-23 campaign, making the PFA Team of the Year and Champions League Team of the Season.
The 29-year-old has and continues to be beset by injury problems at the Etihad, and he only has five appearances to his name in the 2023-24 season so far, but he is a crucial cog in Guardiola's system when fully fit.
Stones - who has a total of 15 goals and five assists to show from 233 matches for the Premier League champions - signed a new long-term extension back in 2021, and those terms do not expire until the summer of 2026.
However, Football Transfers claims that the Citizens are now hoping to tie the former Everton man down for longer and are negotiating an extension with the Englishman's entourage.
While thrashing out the terms of his current deal two years ago, Man City and Stones allegedly came to an agreement that all parties would reconvene to discuss an extension again when the 2023-24 season rolled around.
The ex-Barnsley youngster was already handed a bumper pay rise with his current terms, but the report adds that a renewal would bring him in line with the club's highest earners, such as Erling Haaland.
City head coach Guardiola is said to be pushing for the treble winners to tie Stones down to fresh terms, having labelled the 29-year-old one of his "favourite" players at the club.
Any new terms would supposedly keep Stones at the Etihad until the end of the 2026-27 season, by which time the centre-back - who cost the club £48.2m in 2016 - will be 33 years of age.
Since the start of last season, City have extended the contracts of no fewer than seven players, as all of Kyle Walker, Rico Lewis, Bernardo Silva, Phil Foden, Nathan Ake, Julian Alvarez and Scott Carson have put pen to paper.
Talks with Kevin De Bruyne - whose contract expires in 2025 - are also believed to be in the pipeline, but discussions have supposedly been placed on hold while the Belgian recovers from a severe hamstring injury.
In addition, Man City agreed an extension with head coach Guardiola last year until the summer of 2025, but the report adds that the Premier League champions want to keep the 52-year-old around for longer.
As well as his sustained success on the field, Guardiola is also said to play a key role in negotiations with players over new deals, and the Citizens are determined to secure his services for the long-term.
Man City demolished Bournemouth 6-1 on Saturday to rise to the top of the Premier League table, one point above Tottenham Hotspur before the Lilywhites take on Chelsea on Monday.