Hill also urged Football Federation Australia to give ground to the game's stakeholders saying the current governance model is "unfair, unreasonable and unsustainable".
After failing to reach a resolution on Thursday, missing FIFA's November 30 deadline to sort out the row over the composition of its congress, FFA's fate should be decided next week when the entire board is expected to be sacked and replaced by a 'normalisation committee'.
Hill, who ran football in Australia between 1995 and 1998, believes there is just enough time for the game to save itself from deep embarrassment.
"This is a very sad turn of events," Hill said.
"The clear signals coming from this unresolved situation is that FIFA intervention should be avoided at all costs because it would be a tragic and black day for Australian football if it happened."
"Yes, the deadline has passed but we should be able to sort out our own affairs and I hope FFA can fix this mess in the next few days before FIFA meet next week to decide Australia's situation.
"If FFA resolve the impasse they would be able to say to FIFA that they have reached agreement and that way a much worse scenario could be averted."
Hill recognises that the animosity between the warring parties has reached a level where agreement is difficult but he said Australian football had no choice but to try to save the game in added time.
"They have to have a go at it and sit down and sort it out. There is time," he implored.
"I remember I used to run the railways. I would learn at midday that there would be a strike organised for midnight.
"You had to sit down and try to reach an agreement in 10 or 12 hours because it would be much better than no trains running.
"And this is far more serious than a railway strike.
"It's not easy. If it were easy they would have reached agreement by now but we are now almost at a point of no return."
Hill, who is now an author, said he is still a big fan of the game and could not speak highly enough of FFA's performance in the last decade.
But he said FFA had to learn to give football's stakeholders a greater say in the running of the game.
"FFA have done a terrific job in the last decade or so to advance the game of football in Australia ... getting into Asia, qualifying for successive World Cups and creating the A-League.
"But permanently denying greater representation and democracy is unfair, unreasonable and unsustainable.
"I am the FFA's greatest fan and I've admired everything they've done but they have to give ground here. When I was in football I had a devil of a job progressing the sport because of the opposition from entrenched stakeholders. The FFA have been independent of that and have had a lot done and must take credit for it.
"But no reasonable person would say that FFA can permanently have so little representation and democracy and turn over the directors without there being genuine involvement and voting by the real stakeholders of the game: the federation and the A-League clubs."