Barkley has had an inconsistent season with the Toffees, but Redknapp has seen enough to suggest that he still has a bright future.
He predicts that the England international will rediscover his very best form and thinks that next season could be the one in which he takes his game to the next level.
"Everton have a lot of good young players and Ross Barkley will absolutely fire next year," he said. "I think he has the potential to be one of the best players in the Premier League."
Barkley burst onto the scene last year, when his displays in an attacking midfield role dazzled Toffees supporters.
However, his second campaign as a regular starter has been a challenge - with the burden of expectation seemingly weighing heavy on his shoulders.
There can be no doubting Barkley's quality, though, and Redknapp is right to suggest that he has a massive future.
The 21-year-old is one of the most naturally gifted players in the country and his match-winning ability should take him to the very top of the game.