A number of clubs chasing promotion from League One, led by Peterborough United, have told the EFL the season must be completed, no matter what.
Posh chairman Darragh MacAnthony released a statement on Thursday evening on behalf of his club, Oxford United, Sunderland, Fleetwood Town, Portsmouth and Ipswich Town.
In it, he said: "We have no desire for voiding the season, points-per-game scenarios or letting a computer decide our footballing fate.
"For our fans/staff and for the integrity of our sport, we are all looking forward to completing our pending fixtures/season under guidance from the EFL at a time it is deemed safe to do so."
The intervention came ahead of a crunch meeting on Friday where League One clubs discussed options for completing the campaign with the EFL board.
There had been talk that both the League One and League Two seasons would be cancelled, with many clubs understood to have serious concerns about the financial implications of staging matches without fans.
Watch an interview with Adi Mowles, chairman of the Peterborough Independent Supporters Association
Posh were sixth in League One when football was suspended in March due to the coronavirus pandemic.
Ipswich Town also confirmed that owner Marcus Evans has written a letter to the EFL reiterating the club's desire to complete the season.
Before the suspension, Town had lost their last four games to slip to 10th, but with eight games still remaining, there remains hope within the club that they could still gatecrash the play-offs.
Watch an interview with Ipswich Town fan Benjamin Bloom
Meanwhile, League Two clubs unanimously agreed on Friday that they would like end to their season early.
Clubs also indicated that relegation to the National League should be removed this season, which would mean Stevenage, who are currently bottom, would remain in the EFL.
The final league positions would be decided on a points per game basis, meaning the top three of Swindon Town, Crewe Alexandra and Plymouth Argyle would be promoted automatically, while the play-offs would still go ahead.
Under the PPG method, Colchester United would face Exeter City, while Northampton Town would take on Cheltenham Town.
"Having considered the protocols and costs that would be required to be met to conclude the current season, League Two Clubs have unanimously indicated a preferred direction of travel to curtail the campaign in line with the framework outlined by the EFL Board," and EFL spokesperson said.
"In addition, Clubs asked for consideration to be given to suspending relegation to the National League for 2019/20 as a result of circumstances created where fixtures cannot be completed. No commitments were made in this respect and the Board will now consider the implications of the division’s preferred approach at their next meeting."
However, these suggestions still need to be ratified by the EFL and Football Association.
League One clubs failed to come to an agreement with further discussions due to take place next week.
League One clubs have been given guidance by the EFL to enable them to return to training safely.
The advice includes testing players and staff twice a week, only allowing five players to train on one pitch at one time, and disinfecting all equipment after sessions.
How will clubs return to training safely?
Players and all staff have to be tested twice a week, with no one allowed on site at the training ground unless they have tested negative for Covid-19 48 hours before.
A ‘one way system’ should be put in place at training grounds, while the two metre social distancing guidelines should be adhered to at all times.
Players will have to arrive already changed and bring their own drinks and will be subject to a temperature check and medical questions before being allowed in.
Gyms will be out of use, as will canteens and dressing-rooms, and players will leave in their cars straight after training has finished and shower at home.
Only up to five players will be allowed to train on one pitch and must maintain social distancing. Shooting and one to one goalkeeper work is allowed but no close contact drills.
All equipment must be disinfected between sessions with at least a 30 minute gap between sessions and sessions will only allowed to last for 75 minutes.
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