The treble-winning Celtic boss is set to be confirmed as the new Spurs boss, coming in as a permanent replacement for Antonio Conte, who left the club in March.
The 57-year-old has a big task on his hands in digging Spurs out of their slump as they finished eighth place in the Premier League and extended their trophy drought to 15 years.
But former Spurs boss Redknapp believes Postecoglou is an ideal fit for the north London outfit, thanks in part to a conversation he had when he was managing the Jordan national team in 2016.
When asked by talkSPORT Drive co-host Darren Bent on his initial thoughts on the appointment, Redknapp said: "Yeah, I like it.
"I've said before I met him out in Australia, when I went out and managed the Jordan national team, he managed the Australian team.
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"Tim Cahill played for the Australian team and I was just chatting to him before the game and he said 'our manager's fantastic'.
"I said 'really?', he said, 'Harry, he is top drawer' and that was it. I'd never heard of him at that time... Timmy Cahill said he was brilliant and that's stuck with me. Then I've watched how he's done at Celtic and he's been brilliant, I love him.
"There's no fannying [around] with him, he says it as it is, I like him. He don't care, if a player misses a goal he's not afraid to say 'my old woman could've scored that'."
He continued: "[Postecoglou] will get the message over early. I think the lads will love him, they seem to love him at Celtic."
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The 57-year-old Australian has now agreed personal terms ahead of his move to London.
Now, Spurs are thrashing out compensation with Celtic over the remaining year of his contract.
But Redknapp expects both parties to get a good deal thanks to the pair negotiating the move.
"There'll be hard negotiations going on with Daniel [Levy] and Dermot Desmond," he said.
"Dermot ain't no fool, you'd want Dermot on your side any day. He's a very clever man and Daniel won't walk all over him that's for sure."