Scottish-born Reilly, 71, played for Australia at the 1974 World Cup in Germany and later served as a Football Federation Australia committee member and representative to FIFA.
Speaking at the Whole of Football Fan Forum in Melbourne on Thursday, Reilly expressed a belief that the division of responsibility between FFA and the individual state federations continues to hold Australian football back.
"I believe governance is the main thing that's got to be fixed in football, no question in the world about it," he said.
"The governance structure we've got at this point in time is costing us a fortune. We've got people still using the political environment to remain in positions and doing that at the cost of a governance structure that will stand the test of time.
"It is very, very, very important that we get the right one and there are some people who say there should be one governing body, like the AFL or the NRL. There are significant amounts of money that can be saved. You hold one body responsible, one corporation, one treasury, one governing body.
"When we get to that level, we will be a game that will be feared from everywhere. And, the quicker the better."
Roy Hay, a widely respected Australian football historian, echoed the calls of the ex-Hibernian goalkeeper.
"Jack's absolutely right," he said.
"It's absolutely essential that we do have a governance structure where the tribal council runs the game and the subordinate organisations follow the plan and the model. In terms of aspirations, that's the way we want to go."
FFA chief executive David Gallop acknowledged the issue but flagged a number of obstacles barring the path to such a scenario becoming a reality, at least in the short term, preferring to focus instead on developing consensus and ensuring the respective administrative bodies are clear in their responsibilities.
"I wouldn't suggest it's easy, no," he said when asked about the feasibility of Reilly's suggestion.
"One of the things we started (to aim for was) getting to the stage where each of the layers of governance at least know what their role is and who's paying for what. That sounds a simple recipe. There's a lot of duplication of effort, there's a lot of crossover. That's got to be able to be fixed."