The England international, who is not yet back in pre-season training following his EURO 2016 trip with the Three Lions, has been aligned with a move away from Goodison Park for much of the past few months.
After numerous offers from Chelsea were rebuffed by Everton last year, Man City have emerged as front-runners to lure the ball-playing centre-back along the M62 to the Etihad Stadium, with the Merseyside club rumoured to be braced for a £50m+ offer.
And reports claim that Stones is working hard to engineer a switch away from the club, after asking Moshiri to allow him to move on.
The Iranian billionaire recently purchased a majority share in Everton, and has been largely credited for putting the money in place to lure Ronald Koeman in as Roberto Martinez’s successor.
Although cash is seemingly not an issue for the club now, keeping an unhappy player may prove tricky, especially after last summer’s saga surrounding a proposed transfer to Chelsea.
Stones is understood to be attracted to working under Pep Guardiola and Man City.
Should the Citizens pay £50m for the youngster, the deal will make the 22-year-old the most expensive defender in Premier League history and the most valuable English player ever.