Spurs will be runners-up to surprise champions Leicester City if they draw or win Sunday's final Premier league game at relegated Newcastle United.
Only if Tottenham lose and Arsenal beat relegated visitors Aston Villa will Arsene Wenger's side finish above their local rivals for the first time since 1995.
However, 41-year-old former England defender Campbell, one of the few players to represent both clubs, said one year does not change anything.
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"Power shift is not one season," he told the City AM newspaper. "Power shift is when you've got consistency over a five or 10-year period. There is no evidence yet.
"There is potential, but everybody has got potential. It's all about making it into reality. Come back to me when it's five or 10 seasons and you have consistently played top, top football."
Former Spurs captain Campbell, who made an acrimonious move to Arsenal on a free transfer at the end of his contract in 2001, said that in the same circumstances he would still leave Tottenham but would not join their bitter rivals.
"If I was in the same situation I'd probably move abroad," he added. "The most exciting football is the Premier League but the best football is in Spain."
Campbell was courted by Barcelona when he was deciding which club to join at the end of his Spurs deal.
(Writing by Steve Tongue; Editing by Ken Ferris)
