New City manager Pep Guardiola is keen to make Stones his next high-profile transfer of the summer.
Stones was one of only two outfield players not to see action in England's disappointing Euro 2016 campaign.
Talks have yet to take place, but the asking price would make Stones, 22, Britain's most expensive defender.
Everton have no need to sell, but the possibility is growing that Stones will leave before the start of the new Premier League season.
He was at the centre of a transfer battle last summer when Everton rejected a succession of bids rising up to almost £40m from Chelsea, simply refusing to sell to then manager Jose Mourinho.
Guardiola has made Stones, who has 10 England caps, a priority target as he prepares to renew his rivalry with Mourinho, who is now across the city at Manchester United, and looks certain to get his man.
Manchester City have already signed Ilkay Gundogan from Borussia Dortmund and completed a £13.8m deal for Spain forward Nolito from Celta Vigo after their interest in Euro 2016 was ended by Italy.
Everton will give any money they get for Stones to new manager Ronald Koeman to increase his already considerable transfer fund.
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Manchester City want to buy Everton defender John Stones, but would have to pay the Goodison Park club around £50m for the England international.