Stones has come under criticism for his performances over the past season, which have been rather error-prone.
The 21-year-old has shown some signs of vulnerability in his defending, but England boss Roy Hodgson has kept faith in the centre-back.
Stones is part of the England squad for Euro 2016, and he is in with a chance of starting in the Three Lions’ first match against Russia.
However, Campbell feels that Stones should be left on the sidelines for the international tournament, as he is not ready yet to play a regular role for his country.
“John is one to watch in the future. He reminds me of Alan Hansen,” Campbell said.
“But he has to quicken up his play and make sure forwards don’t think he is always going to play out.
“Clever forwards will suss that. But his time will come.
“He needs to watch more and then eventually he will have his time.
“This tournament might be a bit too early for him.”
Stones was part of an Everton defence which badly disappointed last season.
The youngster is still regarded as one of the brightest prospects in England, however, with his ability in possession earning him a lot of admirers.
Stones has earned 10 England caps to date, and he impressed in the Three Lions’ recent friendly against Australia.
Stones will compete with Manchester United’s Chris Smalling and Chelsea’s Gary Cahill for a place in Hodgson’s starting line-up.