The English Football League says no decisions have been taken regarding the next steps after games were suspended until 3 April because of coronavirus.
The EFL said its board were due to meet again this week and it would continue with its "contingency planning".
A further update will be issued following that board meeting.
"Now is the time for cool heads and calm reflection, rather than speculation," EFL chair Rick Parry said in a statement issued on Monday.
On Friday, all games in England's Premier League, EFL, Women's Super League and Women's Championship, plus in Scotland, Wales and Northern Ireland, were postponed.
The National League decided against such action in their three divisions and six fifth-tier games went ahead on Saturday.
The Premier League said play will resume on 4 April subject to "conditions at the time", although BBC sports editor Dan Roan says resuming on the date is privately deemed "almost impossible".
Football Association chairman Greg Clarke is known to have expressed his fear at an emergency meeting on Friday that the season may have to be abandoned.
Meanwhile, Leeds United chief executive Angus Kinnear has said "there is a groundswell of opinion that the right thing to do is complete the leagues".
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The EFL added: "The health and wellbeing of EFL staff, players, club employees and supporters is of paramount importance and will be key to the decisions made by football.
"It is with that in the forefront of the league's mind that it notes the intense speculation that has appeared across the local, national and international media over the weekend.
"While [we] understand there is a strong desire from both the media and general public to understand what may happen next, there have, at this current time, been no decisions taken.
"The league also feels it inappropriate to respond to the many hypothetical solutions being suggested while the many unknowns remain.
"Given the fast paced environment and parameters we are currently working within, it is simply not practical to give a running commentary on what may happen.
"In the immediate short term we will continue with our contingency planning to deal with the implications the outbreak of Covid-19 has presented the EFL and its clubs, in addition to liaising with the Government, health authorities and football partners.
"A further update will be given once the EFL board has met this week. In the meantime, we wish the football and wider community well and urge all to follow the guidance from the Government provided by Public Health England if presented with any symptoms."
Maintain the integrity of the competitions - Kinnear
Leeds are top of the Championship, seven points clear of third-placed Fulham with nine games of the league season remaining.
Kinnear, who also revealed that some members of staff are self-isolating and the club will be moving to a "skeleton staff" from Tuesday, wants the season to be played to a conclusion.
"At the moment it is a time for cool heads and patience and I don't think we need to jump to any immediate solutions," he said in a statement.
"I think the broad principle is that you maintain the integrity of the competitions and when the time comes and it is safe to do so, you finish the leagues.
"I think everybody is starting to feel this is the right thing to do and it is certainly our opinion; we think it maintains the integrity of the Football League pyramid and the competitions.
"We've heard from Serie A and La Liga who believe that if Euro 2020 is suspended, it could allow a window for leagues across Europe to complete.
"We would like our supporters to be able to witness the rest of the season with us and by playing the games; it also helps the clubs financially, particularly further down the pyramid."