Postecoglou, who guided Scottish club Celtic to a domestic treble, is set to sign a two-year deal to take over Tottenham and become the first Australian to coach an English Premier League side, British media reported.
Though Australia has produced a slew of world-class players, the country's coaches have long been overlooked by major European clubs.
That could be set to change, said Arnold, who matched wits with Postecoglou as opposing A-League coaches for years.
"We’ve got some great young coaches in the A-League and overseas," Arnold told reporters on Tuesday. "Kevin Muscat is doing fantastic (in Japan). These guys will end up overseas. Ange is the leader of that pathway."
Muscat won Japan's domestic championship as coach of Yokohama F. Marinos last year, three years after Postecoglou guided the club to the 2019 title.
Former Socceroos defender Patrick Kisnorbo, who coached Melbourne City to the 2021 A-League title, became the first Australian to coach in France's top flight after crossing to Troyes last year.
"You need someone to open the eyes of people around the world to say, 'Oh, the Australian coaches might not be so bad'," Arnold said.
Arnold backed Postecoglou for success at Tottenham, describing him as a football obsessive who draws motivation from proving people wrong.
"I always knew that he had that mentality of where he wanted to go, that was to the top," he said. "Going to Tottenham I think is a great fit for him and I think he'll kill it."
