The 22-year-old was one of the hottest properties in the transfer market this time last year but his stock has fallen slightly after a difficult season for Everton.
Stones is a talented reader of the game and distributor from the back, but costly errors have left a question mark over his readiness to play at the highest level.
Chris Smalling is expected to take one of the spots in central defence but Roy Hodgson must decide whether to partner the Manchester United man with either Stones or the more experienced Gary Cahill.
Campbell, who played 71 times for England and was named in the FIFA team of the tournament after the 2002 World Cup, has no doubts whom he would pick.
"If you keep making mistakes at international level, you're going to suffer because one mistake in a tournament and you can be out," Campbell, speaking at the William Hill Euro 2016 preview evening, said.
"If you make mistakes at a domestic level, you have more time to learn. He is learning.
"He just has to understand there are moments to play the ball and moments to keep hold of the ball. He just needs to find that balance.
"I personally would go for Smalling and Cahill. I would go for the experience of those two guys.
"For me, something drastic would have to happen for Stones to start. You start with your most solid back four and go from there."
England will head to France with an exciting wealth of attacking options, with Harry Kane, Jamie Vardy, Wayne Rooney, Dele Alli and Raheem Sterling just some of those vying for starting places against Russia on June 11.
At the other end, choices are fewer. Gone are the days when Campbell was fighting off John Terry, Rio Ferdinand, Jamie Carragher and Ledley King to play in defence for England, and he believes the national team's lack of options now is symptomatic of the game more generally.
"Football has changed," Campbell said. "Players want to go forward all the time.
"There are so many attacking midfielders. Then there are centre-backs who want to be defensive midfielders and full-backs that secretly want to be wingers.
"When I played I didn't mind right-back and left-back going forward but one would stay and one would go. Now they both go. What is going on?
"Leicester have shown that a solid back four and people knowing their positions is key. You need to be flexible at the right time, not just, 'I want to go, go, go'.
"You'll get clever forwards exploiting those spaces so you have to get the balance right."
Hodgson's own future is also on the line this summer given his contract expires after the tournament and the Football Association plan only to review it once the competition is finished.
Campbell believes England can make the final but says reaching the last four is a must.
"I think England will get to the final, I really do," he added.
"Success for Hodgson is semi-finals plus. You have to look at what he has done, he ticks a lot of boxes for the FA, but he has to at least take England to the semi-finals.
"You need to see progression and this England squad, which is an exciting squad, deserves progression in all departments."