The governing body has said a decision on Ange Postecoglou's replacement isn't likely until February, with Australia's next match not until the FIFA international window in March.
But Slater labelled the selection process, which involves former Socceroos stars Mark Schwarzer, Mark Bresciano and Stan Lazaridis, a disgrace and said it lacks transparency.
"Getting a national coach would be a priority, you would think?" Slater said on the Big Sports Breakfast.
"Even though it’s 2018 and we’re only six months or so away from the World Cup, (the FFA) couldn’t get a teabag out of a teacup at the moment.
"They can’t name a national coach. It’s an absolute disgrace and we’re not hearing anything from anyone.
"Time is running out and in some ways has run out."
Several high profile overseas coaches have been linked with the Socceroos job through the media including former Manchester United boss Louis Van Gaal, ex-England manage Sven Goran Erikkson and World Cup winner Luiz Felipe Scolari.
Sydney FC boss Graham Arnold is favourite for the role, but according to Slater, no Australian coach has been formally contacted about the position as of yet.
Slater believes the FFA won't find a foreign coach that fits their criteria and mocked the reported contact with Dutch manager Van Gaal.
"I'm hearing that people they are interviewing – some of the names make me shake my head," Slater said.
"The coaches that are available are either the ones that are semi-retired or ones that have lost their job because of poor performance.
"No local Australian coach has been approached or interviewed.
"(Louis Van Gaal) would be great wouldn’t it? A massive name in world football. He knows a lot about us, doesn’t he?
"Two of the criteria is you got to know the players and you got to know the culture. There is no overseas coach that can answer yes to both those criteria."