Stones is a target of Premier League Champions Chelsea.
Stones is the subject of interest from Chelsea, with the Guardian reporting that a third bid for the defender in the region of £30 million is expected to be made by the Premier League champions.
Stones played the entire 90 minutes of Everton's opening day draw with Watford at Goodison Park and appears to have told the 21-year-old to just keep on doing what his normal thing.
The Everton skipper is quoted in the Liverpool Echo, saying: “He is dealing with it really well. It is nice when people want you and all sorts, but it is a bit mind boggling when all sorts of numbers are thrown in the papers. It is strange the way the transfer window is open while the season starts.
“It is a little bit of test for him now.
“It is a test of character and we all know he has a good character. He is a level-headed lad. It is easy for people to let it go to their heads or decide not to be totally committed."
The worrying aspect of the quotes in the article is that there doesn't seem to be much of an urge from Jagielka to keep Stones at the club, and instead he expresses the flattery that another club in the division is interested in his services.
As it stands, it would seem better for Stones' development if he remained an Everton player.
Even if he is viewed as the long-term replacement for John Terry, he still faces stiff competition from both Gary Cahill and Kurt Zouma to get into their starting XI in the immediate future - but the experience in the Champions League could add another element to his game.
There is a worry for Everton that they could lose one of their best players, and there will be a lot of scrutiny as to how they spend the proceeds should the transfer go through.