'Sky Sports' is reporting that Manchester City's owners believe that a deal can be done within the next few days.
Last week, it was reported that Manchester City would not pay the £50m asking price for Stones as City only valued the defender at £40m.
However, 'Sky Sports' now says that Everton will receive a fee somewhere near their asking price.
Stones is said to favour a move to the Etihad and Everton may finally be resigned to losing the man they tried so hard to keep hold of last season.
It is set to be a busy week of negotiations for Manchester City, with Leroy Sane in Manchester to discuss a deal with the club.