Off contract at the end of June, the England defender is set to leave City as a free agent this summer.
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The Athletic says City will announce next week that Stones will be leaving the club. City did something similar for Bernardo Silva last week.
Stones has made 292 appearances for City since signing from Everton in 2016.
The 31 year-old has won 18 trophies as a City player, including six Premier League titles, the Champions League and the Club World Cup.