sideJohn Stones was part Fußballtrikots Kinder of England's Euro
City have already completed the £21m signing of Ilkay Gundogan from Borussia Dortmund and a £13.8m deal for Nolito from Celta Vigo.
Everton rejected a Chelsea bid of £26m for Stones last summer and City are expected to have to pay considerably more.
There have also been reports in Italy that City are interested in Juventus defender Leonardo Bonucci and made a £38m bid which was said to have been rejected by the Serie A side.
John Stones was part trikot Polen
of England's Euro 2016 squad but did not play before the round-of-16 exit.
Everton centre-back Stones, 22, has been identified by Pep Guardiola as a priority but could cost up to £50 million.
New City boss Guardiola is determined to sign a top-class centre-back but missed out on Athletic Bilbao's Aymeric Laporte earlier in the summer after the Frenchman opted to sign a new contract.
However a source has told ESPN FC that the club have not made any trikot Schweden
offer for the 29-year-old Italy international.
The England international had been at Euro 2016, although he did not make an appearance, but City are now ready to begin negotiations following the nation's elimination from the tournament last week.
Everton are now bankrolled by British-Iranian billionaire businessman Farhad Moshiri and do not need to sell Stones but the Daily Mail has reported that Stones has told new Toffees boss Ronald Koeman that he wants to leave the club.