The Italian has taken charge at troubled giants AS Roma, who are Spurs' next opponents.
The two clubs will go head to head in London in the Europa League on Thursday night.
Speaking about Ranieri, Postecoglou told reporters: “It’s unbelievable. It just goes to show the passion he has for the game. I’m sure there are more enjoyable ways to live his life now but he still has it in him. I’ve not come across him before but I’m looking forward to saying hello.
“It’s always nice to meet people who’ve made a massive impact on football, particularly managers. He’s always come across as a gentleman. I’m looking forward to meeting him. It just goes to show that bug you have as a manager, for being on the touchline, doesn’t leave you.”
Asked if Ranieri winning the Premier League with Leicester was inspiring, he added: “I don't know if it's inspired but certainly it's what I love about football. There aren't many sports where that can happen, such an unlikely story of a club and a manager, who had already had a really strong reputation, it comes together like that in the biggest league in the world.
“It's a hell of a story. It's one of those where if you saw it in a move, you'd think great movie but ahhh it's never going to happen. And it did. Everyone who lived that experience within Leicester football club and everyone associated with the people in there and for Claudio and his family... That's all we crave, just to leave some sort of imprint and footprint in our careers that lasts beyond our ability to do what we do, he's certainly left an enormous footprint with that season at Leicester.”