FA chairman Greg Clarke has warned the association's Council members against embracing Project Big Picture.
Driven by Manchester United and Liverpool, Project Big Picture would see power in the Premier League consolidated among nine clubs instead of all twenty.
The EFL Cup and Community Shield would both be abolished, and the Premier League itself would be reduced from 20 to 18 teams.
EFL clubs - led by group chair Rick Parry - have backed the proposals, which would see 25 per cent of the Premier League's annual revenues doled out to sides below the top tier. A £250million payment would also be made up-front.
But Clarke has told the FA Council to be wary of "short term decisions that would be damaging in the long term".
Ahead of Thursday's planned Council meeting, Clarke said, "Both the Premier League and the FA support a wide-ranging discussion on the future of the game, including its competition structures, calendar and overall financing, particularly in light of the effects of COVID-19.
"Our perspective is that we have a fantastic league structure and pyramid that is the envy of the world. While we should always be open to evolve, to move the game forwards, changes have to be done in the right way and with a long-term perspective in mind."
Clarke admits to taking part in primary discussions around Project Big Picture - with the knowledge of senior FA board members and CEO - but got cold feet when he says, "The principal aim of these discussions became the concentration of power and wealth in the hands of a few clubs with a breakaway league mooted as a threat."
Several EFL clubs find themselves in dire financial straits, with gate receipts non-existent since March.
Some could find themselves going the same way as Macclesfield and Bury and vanishing altogether if money doesn't start rolling in at the turnstiles soon.
"We are fully aware that there are huge financial pressures throughout the game and collectively we need to work hard so that our clubs survive the pandemic," Clarke wrote, "However, we must separate this need from discussions about the potential long-term structure of our wonderful game.
"Of course, if we can agree changes that are beneficial in the long term and have an immediate positive impact, we will consider that."
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