However, despite his track record, Keane feels that Peters ought to keep a low profile whilst out in Brazil.
He told The Mirror: "The sports psychologist should be the manager. Brian Clough was the best sports psychologist for me and Alex Ferguson was good.
"I heard Peters speak at Wembley two years ago and we should be open-minded and not knock it.
"But don't think, for one minute, that if it gets to penalties in an England game that the players on the pitch are going to look over and forget about Roy Hodgson and look where Steve Peters is and go, 'The chimp is out'."