The 18-year-old, who made his first-team debut for the club last month, has been linked with a host of Premier League clubs, but Georgina Lillis has denied that the youngster will make the move.
"There has been a lot of unwanted paper talk with regards to John. It doesn't benefit the club and it doesn't benefit John. Just because a scout is seen in the stands it doesn't mean a player is on the move next window," Lillis told Sky Sports News.
"John is at a point in his career where he needs to be playing first team football and to keep developing as a player. Barnsley is doing just that and valuable experience with England is helping him progress.
"If there is any interest or approach from Premier League clubs for John then that's between them and Barnsley. Of course John wants to play in the Premier League but what's most important, at this stage, is that he doesn't get his head turned and keeps working hard and improving."
Stones has made 12 first-term appearances for the Championship club.