Their financial troubles and collapse to the third tier of English football has been attributed to chasing the dream - but Spurs are looking to finish in the top four of the Premier League in a different way.
An example of that is Redknapp preparing to ditch his interest in Ruud van Nistelrooy as the wage demands of the Real Madrid striker are too high.
"The chairman runs a well-run club," said the Spurs manager. "He runs it right. We are not gong to spend crazy money on players who are 30-odd years of age, pay them crazy money and there is no return on your money.
"But if I really want a player, the chairman does everything in his power to get him for me. If he is too expensive then he says 'Harry I can't do a deal with them'."
Redknapp believes Leeds could return to the top flight within two seasons under chairman Ken Bates, who he encountered in 1988 when his Bournemouth side defeated Chelsea.
"Someone asked me if I would let my chairman go on the bench, I just replied that my chairman would not want to go on the bench," Redknapp said. "Ken sent me a rather nasty letter giving me some grief about saying that.
"Then, in 1990 when I had a road accident in Italy and my mate Brian Tiler was killed, we had a dinner in Bournemouth to raise some money and Ken came along and was fantastic.
"He bought everything in the auction for four times more than any one else was willing to pay, without letting anyone know it was him. He was fantastic and I will never forget that."
Redknapp expects Simon Grayson's side to offer a stern challenge.
Aaron Lennon will miss the tie against his former club as he has a groin injury - but another ex-Elland Road winger, Danny Rose, could make his first start for Spurs.
"I loaned him out to Peterborough earlier this year but his attitude has changed, he's worked hard and he's got terrific ability," said Redknapp.
Rose's opportunity could be interpreted as a blow for David Bentley, with Redknapp hinting at the winger struggling in training.
"He is here and he has to work hard to get in the team," Redknapp said. "That is all I ask them to do, come in every day and train hard, work hard. They have a fantastic living so it is not a lot to ask, is it? Come in every day and train hard and show a good attitude."
Attitude is not a problem he finds with Croatia midfielder Niko Kranjcar, who has been ahead of Bentley in the pecking order while Lennon has been sidelined.
"Niko works hard, trains hard and never gives a minute's problem - no attitude," Redknapp said.
"Luka Modric is the same. That is what I enjoy about still being in football, players who want come in every day and train and enjoy it and play well. That is really what keeps me going in it."