The Blues defender is a top target for new manager Pep Guardiola.
The England international has been linked with a move away from Goodison Park for several months, with Pep Guardiola keen on bringing him to Manchester.
The former Barcelona and Bayern Munich coach reportedly views Stones as the perfect addition for his new look City defence.
So far no formal bid has been made, but all suggestions have been that Toffees boss Ronald Koeman will demand £50 million for his star defender.
However, according to the Daily Mail, that is a price even Manchester City are reluctant to pay outright for him. Instead, they have offered a player plus cash deal as they seek to strike a deal with the Toffees.
The player is allegedly keen on the move, having grown disillusioned at Everton, and believes that working under Guardiola will make him a much better player.
The Blues have finished 11th in the Premier League for the last two seasons, and Stones in particular came in for constant criticism for his performances last year.
Koeman has now replaced Martinez, but it seems that has not been enough to convince Stones to stay on Merseyside.