Postecoglou was announced as Spurs manager on a four-year deal on Tuesday and will take the reins on July 1, becoming the first Australian to lead a team in the top flight of English men's football.
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City and Marinos played a friendly, which the English powerhouse won 3-1, but the Japanese club had 58% of possession.
"I was lucky to meet him in Tokyo years ago when he was manager at Yokohama, one of our clubs in the City Football Group, and it was an interesting chat.
"I have a good relationship with the owner of Celtic. He did an incredible job [at Celtic] and he will do an incredible job for Spurs.
"Hopefully, we can score one goal away."
Guardiola's late quip referred to City's inability to win games at Spurs in recent years.
Based on that 2019 friendly, Postecoglou, who is relentlessly attacking-minded and focused on possession, isn't going to take that approach.
"People will say it was a friendly game, in preseason, they didn't take it too seriously but I would hazard to guess how many times a team coached by Pep has been out-possessed," Postecoglou told Optus Sport after that 2019 friendly.
"I hear people say possession doesn't mean anything. I think it does, particularly when it is possession in meaningful areas, not just at the back, and creating problems.
"But it takes a bit of courage and conviction to take on a team like City or coached by someone like Pep -- because there is the fear that if it goes really badly you can be very exposed."
Postecoglou believed that level of fear stopped teams from challenging City and played into their hands but wanted his side to test themselves and the Premier League giants.
"From both sides of the game they walked away knowing, of course it was a friendly, but understanding that even the very best can be tested if you believe in something," he said.
"The teams I coach believe that if you play this way, you don't adjust it and you don't have any fear or hesitation because of the opposition."