Kane, who netted 41 times for club side Tottenham Hotspur last season, currently tops the World Cup scoring charts after scoring five goals in two games.
Redknapp, speaking to Sky Sports News, said that Kane has elevated his game to become one of the top five players in the world.
"He is our Messi, our Ronaldo. He is the talisman, the person we will be looking at to score and to make that difference," the former player said.
"He is leading by example. He is the player that everyone is talking about - wherever you go at the moment, people from all around the world.
"He has gone to another level and elevated his game. Not only that but as a person and everyone thinks he is one of the best players in the world now - he is in the top five and things can only get better."
Kane is expected to feature in England's last-16 clash with Colombia on Tuesday after being rested for the 1-0 defeat to Belgium.