The 62-year-old has turned around the fortunes of the North London club in his 12 months in charge after guiding a struggling side towards the top of the table.
With that task complete, Redknapp has again sounded his aim to break into the top four of the Premier League, a target Spurs have often set but failed to achieve.
He told Sky Sports News: "There is no reason teams cannot break into the top four if you sign the right players and get the right team.
"Anybody can produce a great team. If you have got the resources, and Tottenham have got the resources, you can be up there challenging.
"It's a great club. Let's hope they can achieve Champions League football. I'd certainly like to achieve that in my time here."
Lasting legacyRedknapp is also hopeful he can create a lasting legacy at Tottenham for the man who eventually succeeds him.
He added: "You would like to think that you can produce teams and leave the club, when you eventually do leave, with a great team and great young players who are coming through.
"That has really got to be my job. Whoever comes in has got a very, very good team."
Redknapp is expected to retire when he leaves Tottenham, but the former Portsmouth boss insists he has no plans to quit the game in the immediate future.
He added: "Sir Alex (Ferguson) is still going strong, Arsene Wenger is still going strong.
"There is no reason why you can't if you still feel good and still have the enthusiasm and love for the game. You cannot beat experience."