It has been reported that Stones will hold talks with City manager Guardiola over his future next month.
However, according to the report, the England international central defender does not want to leave the Citizens and wants to prove himself at the Etihad Stadium.
Earlier this month, The Sun claimed that Everton and Arsenal are interested in signing the 26-year-old centre-back from Premier League rivals City this summer.
Everton return or Manchester City stay?
Stones has not progressed much at City and is not guaranteed a regular place in the starting lineup when he is fit.
True, the 26-year-old centre-back has had injury problems, but he has made some costly mistakes when he has played.
However, City are a massive club who will need a strong squad next season to win the Premier League title, and working with Guardiola is only going to make Stones better.
A return to Everton and working with Carlo Ancelotti would make sense, but perhaps the Englishman should stick it out at City for one more season at least.