Redknapp wants his side to qualify for the Champions League by finishing in the top four, and defeating Arsenal in this weekend's north London derby is the first hurdle.
With Spurs fresh off the back of three straight league wins, Redknapp is confident of a good result going into Sunday’s league meeting at White Hart Lane.
Redknapp told The Daily Mirror: “I think we can overhaul Arsenal.
“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.”
The Spurs boss, whose team are two points ahead of their local rivals with a game in hand, also gave under pressure Arsene Wenger his backing, saying he is "one of the best" managers around.
“He is top class. He knows the game and they will be bang there again," he said.
“I can understand what Wenger is going through, it must be a nightmare for him because he has never had it before.
“People said that we were all jumping around like idiots and that Arsene was just sitting there like a chess grand master.
“Now? Suddenly you get beat and he is jumping around like the rest of us!
“But he is a fantastic manager. He is one of the best in my opinion.”