The 63-year-old is at his fifth and final club after 27 years as a manager. And he reckons when he finally retires, he will now be remembered as the man who returned under-achieving Spurs to European football's elite.
"At least I can always say to the grandchildren, 'We finished fourth one year when I was at Tottenham, we got into the Champions League'," Redknapp reflected.
"You just want to leave the club having done the best you can do - you can't do any more really. That's why it's nice to finish fourth."
He added: "All you can do is keep doing your best, play good football, which is the key to the way we play."
Redknapp has one year left on his contract at Spurs and denies reports claiming he has been offered an extension to his deal by chairman Daniel Levy since Wednesday's 1-0 win at Manchester City, which secured the club at least a top-four finish.
"If the chairman wants to extend my contract, I'd be delighted to, but I'm not going to be chasing the chairman to do it," said Redknapp, whose team take on Burnley on Sunday. "If he wants to, I'm happy; if he doesn't, then it's not a problem. And if I don't, well he won't have to pay me up. I'd walk away and pack up."
Before he does eventually retire, Redknapp will finally be able to have a crack at the Champions League, for which Spurs have qualified for the first time in their history.
Redknapp has talked about the possibility of perhaps signing one "special" player and will in the close season give Levy the names of a couple of transfer targets. But the former Southampton and Portsmouth boss feels the current squad is good enough as it is, if only they can avoid injuries.
"We've got enough but it varies, that's the problem," he said. "A couple of weeks ago we had all kids on the bench, then against Man City suddenly we've got an unbelievable bench - we had Jermaine Jenas, David Bentley, Eidur Gudjohnsen, Roman Pavlyuchenko, Wilson Palacios and Sebastien Bassong.
"We'll be okay, we've got enough strength in depth and we've got one or two young lads who I like who are coming through."
Source: PA
Source: PA