The England international has fallen down the pecking order under Pep Guardiola and was restricted to just 16 Premier League appearances during the 2019-20 campaign.
Furthermore, with the recent arrival of Nathan Ake from Bournemouth on a five-year deal, it is looking increasingly likely that Stones will head for the Etihad exit door this summer.
According to The Mirror, Frank Lampard is an admirer of the centre-back and believes that Stones can come good at Stamford Bridge.
However, the report claims that Chelsea will refuse to pay more than £20m for the 26-year-old, who joined Man City from Everton in a £47m deal back in 2016.
The former Barnsley man will see his current contract at the Etihad run out in 2022.