Championship clubs hope to gain government clearance for a 25 May return to regular training, as part of plans to resume the 2019-20 season.
It is understood a target restart of 6 June has been discussed but clubs still anticipate a more likely 13 June date, in line with the Premier League.
All 24 clubs held a conference call on Wednesday, after an EFL board meeting.
League One and Two clubs will speak on Friday, when the prospect of ending the season seems certain to move closer.
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The plan for the Championship is still to complete the season, thereby avoiding avoid a potential legal minefield around promotion and relegation if the campaign ends early but the Premier League plays to a conclusion.
BBC Radio Manchester has acquired a copy of the EFL's 'return to training' draft protocols, which are based around current government guidelines for Covid-19 protocols.
These requirements are very similar to those of the Premier League, around disinfecting football equipment, keeping communal areas of the training ground such as gyms and changing rooms closed, and no tackling or contact sessions.
- Clubs must appoint a specialist Covid-19 officer, and draw up an operational policy which players and staff must sign
- Twice weekly coronavirus antibody tests and temperature screening protocols for players and staff - a positive test means the training group self isolates for 14 days
- Players must arrive already changed and provide their own drinks
- No 'manual therapy treatment' such as massages. Only essential medical treatment allowed with minimum staffing and provision of personal protection equipment
- All tactical sessions and session planning that does not require physical presence should be done by tele/video conference
- Training will be phased, small groups through to full squad sessions. Each training group allocated one pitch, and maximum of five per group, plus three staff. Seventy-five minutes per training session. Thirty minutes' gap between each training group session
- No tackling, opposed activities of any kind or congested training are allowed
- Clubs can provide takeaway food options for players
An EFL statement, released following Wednesday's board meeting, pointed to a need to acknowledge the financial shortfall that would accompany the game restarting behind closed doors.
While the resumption of competition would satisfy commitments to broadcasters, the costs related to meeting hygiene and testing protocols, as well as a lack of regular matchday income, have to be taken into account.
"The EFL will continue to undertake consultation with our members before the next steps are determined," the statement read.
"Current attention is clearly on the immediate next steps, but the long-term impact on the league and its clubs remains as stark as previously outlined, and solutions are still required to fill the financial hole left by the crisis. The consequences of the Covid-19 pandemic will not be rectified simply by a return to play behind closed doors.
"In addition, the EFL is mindful of the pressing need for clarity in a number of areas, including the practicalities and timeframes of clubs being able to facilitate a return to training. To address this, clubs have today been issued with the latest draft of the EFL's 'return to training protocols', so that they can prepare appropriately.
"However, until all outstanding matters are concluded, including finalising a comprehensive testing programme on matchdays and non-matchdays, the EFL board has informed its clubs that a return to training should not take place until 25 May at the earliest."