A legend of the Hungary side of the early 1950s, Puskas won three European Cup titles and five LaLiga titles with Los Blancos -- possessing what Madrid's website describes as "the best left foot to have graced the Santiago Bernabeu Stadium."
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He later served as Postecoglou's coach at Australian side South Melbourne Hellas from 1989 to 1992, securing an Australian crown in one of the most famous Grand Finals in Australian football history in 1991 along the way.
With Puskas possessing a stronger grasp of Greek than English when he arrived Down Under thanks to a previous stint coaching Panathinaikos, Athens-born Postecoglou served as the Hugarian's translator, as well as his starting left-back, chauffeur, and captain.
"It was more his impact as a person," Postecoglou told ESPN in an exclusive interview.
"Because he's one of the world's greatest footballers and he showed us that irrespective of your stature or what you've achieved, you can still be a decent person and gain respect by just treating people as you would anyone else.
"The way he treated us, there was never any arrogance about him. He cared about us as people and we ended up -- we were a pretty young group -- we ended up winning the championship because we wanted to play for him.
"And I think there's a lot in that, you need to have a connection between the manager and the players. And he did that, just through being a really humble, respectful person.
"As I've grown older and realise that I've had the absolute privilege of sharing a dressing room with one of the greatest footballers of all time, the impact he had on me was to show me that he was still a decent person within that."
Madrid will host already-eliminated Celtic on Wednesday night knowing that a win will seal top spot in Group F.