As the two sides prepare to do battle for the first time in 2011-12 this weekend, the Spurs boss hopes his players can finish above Arsene Wenger's hopefuls for the first time since 1994-95.
At this early stage of the season, Tottenham already have a two-point advantage and a game in hand over the Gunners, and whilst Redknapp wants to put things into perspective - he also wants to take that confidence into Sunday's encounter at White Hart Lane.
"I think we can overhaul Arsenal," he told the Daily Mirror. "It will be tight but I would never write Arsenal off. Sometimes when things go wrong, you know what it is like - everything goes wrong.
"There is nothing that you can do right. Arsenal have had one of those starts - two own goals, you name it - but they have got good players."
Having endured his worst start to a league campaign since first joining Arsenal in 1996, Wenger has the support of his opposite number, who can sympathise greatly with the master tactician after being on the wrong end of thumping defeats in Spurs' opening two games this term.
"I can understand what Wenger is going through," Redknapp continued. "It must be a nightmare for him because he has never had it before.
"I have always said that when Arsene first came here all the other coaches were condemned. People said that we were all jumping around like idiots and that Arsene was just sitting there like a chess grandmaster.
"It was as if he was a professor of chess sitting there as if he was studying every move while these other idiots are shouting and screaming, but if you were winning every game of course you could sit there with your hand behind your head asking your number two: 'What's the score? Three-nil? Oh, wake me up when we get four!'
"Now? Suddenly you get beat and he is jumping around like the rest of us! But he is a fantastic manager. He is top class. He knows the game and they will be bang in there again. He is one of the best in my opinion."