With reports suggesting live sport could resume in a number of weeks in the UK, the EFL said its own position remains unchanged.
The EFL has pledged to have rigorous coronavirus testing in place before its leagues resume in England, and insisted the return of football must not negatively affect key workers.
Reports on Saturday suggested Premier League football may return within weeks with matches taking place behind closed doors.
The UK government is said to have begun looking at proposals for the resumption of live sport as part of a bid to boost morale during lockdown as a result of the coronavirus pandemic.
The EFL said its own position regarding the return of action in the Championship, League One and League Two remains unchanged and that football will only resume when it is safe to do so.
An EFL statement read: "The position of the EFL remains unchanged in that the priority is to resume the 2019-20 season as soon as it is possible with matches only returning at an appropriate point and based on guidance from the relevant authorities. The health and well-being of the nation has to come first.
"Clearly, before any return to football can take place, suitable testing arrangements for participants must be in place and this is core to our current planning, as is ensuring there is absolutely no negative impact on the country’s front-line workers, the emergency services, league and club staff members.
"The EFL's medical advisor is working with a select group of medical professionals and sports scientists to ensure their collective expertise is utilised to address these issues. This group will consider the latest medical information and evidence from both in the UK and abroad, particularly around the viability and accessibility of the various COVID-19 tests that are currently available."
The EFL has been suspended since March 13 and the body's chairman Rick Parry said last week matches will likely take place behind closed doors with the intention to finish the 2019-20 season when it is deemed safe to do so.
Saturday's EFL statement added football can only resume successfully with a "collaborative approach with all stakeholders, including the Premier League and Football Association".
The scheduling of fixtures, promotion, relegation and the opening and closing of transfer windows are among issues the EFL said remain under discussion.