The English centre-half has enjoyed a renaissance this season, after falling out of favour with manager Pep Guardiola last season.
The 26-year-old is set to get a bumper £150,000-a-week contract, which would be worth £39m in total.
Stones and City are preparing for a Champions League semi final first leg against Paris Saint-Germain this week, after winning the Carabao Cup final against Tottenham on Sunday at Wembley.
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