Schwarzer will assist Football Federation Australia select who will take the country to next year's World Cup in Russia and he wants the new coach to go a step further than Ange Postecoglou.
Appointed before the 2014 World Cup, Postecoglou oversaw successful 2015 Asian Cup and Russia 2018 qualification campaigns before quitting last month.
"In an ideal scenario, you want someone long term," retired goalkeeping great Schwarzer told 3AW.
"You want to be able to put someone in place who is pretty much for the next four-and-a-half years because you don't want to be in the same predicament in four years' time.
"What you want is a manager, I think in the ideal scenario, is someone there to 2022.
"To go through the whole process, Asian Cup in between, qualify for Qatar 2022, then take the team there."
Schwarzer, who sits on an advisory panel alongside former Socceroos teammates Mark Bresciano and Stan Lazaridis, has previously backed Sydney FC coach Graham Arnold for the job ahead of high-profile foreigners.
The former English Premier League stopper praised Postecoglou's commitment to building a squad and strategy over a long period.
"I think over the last four years there's been such a big turnaround in the style the Socceroos play, the regeneration of the side, and it's important that continues," Schwarzer said.
"Of course, you're not going to find a replica of Ange, which you don't want.
"You want something a little bit different.
"Someone who'll give you a little bit of their own play on things and add their own mark on how the Socceroos are playing."