Kogan said the clock is ticking on the Premier League and EFL, which controls the three English divisions below the top flight, to break an impasse and agree a fresh financial deal as rolling over of the existing 2019 agreement was "to no one's satisfaction".
He added the regulator could intervene in the absence of an agreement but he would rather the leagues came up with their own solution to the issue.
There have long been concerns that the huge revenue gap between the Premier League and the second-tier Championship encourages clubs to take financial risks in order to reach the top flight or safeguard their place among the elite.
Questions have also been raised about 'parachute payments' which give clubs relegated from the Premier League a cash injection, which may give them an advantage over their Championship rivals.
"The current system bakes in risk," Kogan told the Financial Times Business of Football Summit in London on Thursday. "Multiple clubs throughout the pyramid have told us they would not be able to survive a month if their owner stopped funding."
He added: "We know that players' wages have been rocketing in the Premier League, but it's also happening across the pyramid.
"Relegation, for many, is a near-death sentence. Clubs facing relegation can see their revenues cut by up to 80 percent if they fail to bounce back quickly, and the early analysis we've done suggests this is just as much of a problem between (fourth division) League Two and the (fifth-tier) National League as it is between the Premier League and the Championship.
"The whole pyramid is facing a series of cliff edges," he insisted. "The clock is ticking."
Kogan, speaking later Thursday to reporters, said: "Parachute payments are not going to vanish overnight.
"Clearly there's going to be a discussion about that. What those discussions lead to, I'll tell you when they happen."