And the EFL wants an independent regulator or the Football Association to have backstop powers allowing it to impose a settlement "in perpetuity".
The chairs and chief executives of the EFL, Premier League and Football Association held face-to-face talks on the 'New Deal For Football' package, which if agreed would lead to the biggest governance changes in the English game for 30 years.
However, in a circular sent to EFL clubs this week prior to Friday's meeting, the league said it is still "not hopeful" of securing the financial distribution settlement it is looking for - a 25 per cent share of pooled broadcast revenue with the Premier League, merit-based payments across all four divisions and the abolition of parachute payments to clubs relegated from the top flight.
The EFL is holding a series of regional club and MP meetings at Westminster next week which were originally due to take place towards the end of last year. The aim of the meetings is to cement cross-party support for implementing the key recommendations of the fan-led review, which included at its core the creation of an independent regulator.
"In reality, the EFL is not hopeful of a solution being reached within football," the circular, seen by the PA news agency, states.
"(The EFL) has virtually no leverage that it can use to achieve a positive outcome from the Premier League. In monetary terms, the gap in annual revenue between Premier League clubs and EFL clubs is vast. Not only is this the problem that we are ultimately seeking to resolve, but it is also indicative of the gulf in bargaining power between the two organisations.
"Ultimately the current impasse can be no great surprise to anyone. What the EFL is effectively asking for through its 75/25 model and 2:1 merit payments is for Premier League clubs in the lower reaches of the competition to take less money while they are in the top-flight - and to forego the substantial competitive advantage they get from parachute payments if relegated - in the wider interests of the football pyramid.
"Therefore, it is likely to be only institutions that are independent from football itself, and with a wider remit, that will be capable of making a decision that is in the broader interests of the game. The EFL believes that the issue of financial distributions is so central to the idea of delivering sustainable football clubs that it should be at the heart of the Government's approach to this issue.
"It is therefore something of a disappointment that, to date, the Government, having argued that football is incapable of resolving the game's governance issues (and therefore needs an independent regulator) believes it somehow capable of resolving the even more complex financial distributions issue when the evidence of the last 30 years would suggest otherwise.
"The EFL would support giving the regulator a backstop power in perpetuity to define a fair outcome where there is no agreement, or alternatively finding a way to give the FA that same responsibility."
The Government is expected to publish a White Paper on the independent regulator before the end of the month. It was initially due last summer but was delayed by political upheaval within the Conservative Party.
Premier League chief executive Richard Masters has previously stated it would be a "disaster" to award the EFL a 25 per cent split of pooled broadcast revenue.
Nevertheless, the six chairs and chief executives are understood to have held open and constructive talks on Friday and will continue to meet to explore football-led solutions to resolve wider issues facing the game.
The 'New Deal' is designed to be a comprehensive way forward for the game, covering financial cost controls as well as distribution and also looking at calendar issues, with UEFA's men's club competitions set to expand from 2024. Premier League clubs are understood to be virtually unanimous in their desire to see FA Cup replays scrapped, while the future look of the Carabao Cup is also part of the discussion.