An escalating amount of new cases has clubs worried, and they want to develop a plan.
With nine games postponed over the past week, including five already from this weekend's 10-match fixture list, clubs want the chance to discuss their options to deal with an outbreak of Covid-19 in clubs.
Brentford boss Thomas Frank led calls for all matches to be called off until Boxing Day to enable a reset.
Some think that break should be longer - but others like Liverpool's Jurgen Klopp do not believe it should happen at all; instead touting the need for vaccinations and booster shots.
Arsenal boss Mikel Arteta said clubs need "clarity" about the situation.
Speaking before his side's trip to Leeds, which is one of two games still scheduled to be played on Saturday, Arteta said: "The regulators will make the decision over whether a game is played or not but we all need to understand the reasons behind it. We are going to have to find a way. We knew when we started the season this [Covid problems] could be a possibility and I am sure there was a Plan A, B and C. We have the African Cup of Nations as well, we know the date of the World Cup coming, so we need a flexible calendar now because this world is not the world we used to live in a few years ago. We need clarity."
Meanwhile Manchester City cancelled manager Pep Guardiola's press conference to look ahead to his side's trip to Newcastle United.
The City boss was due to speak to the media on Friday to preview Sunday's game.
However, Guardiola returned an inconclusive coronavirus test and is now waiting for the results of a follow-up PCR test.
Guardiola said on Monday that some staff members at City had tested positive but his side were able to play their Premier League game against Leeds on Tuesday, which they won 7-0.
Anecdotally, Manchester City women's team has postponed an FA Women's Super League match against Reading.
The Premier League said on Thursday it intends to carry on playing matches as long as it is safe to do so.
The meeting itself will not purely be centered around matches being called off and whether there is a break or not. There are also issues around re-arranging the games that have already been postponed.
In addition, there are concerns over player release for next month's African Cup of Nations and the January World Cup qualifiers that cover every continent other than Europe.
"We need clarity" - Mikel Arteta, Arsenal Manager
The release of the Nations League fixtures by Uefa on Friday underlined the issues surrounding the crowded match calendar.
England play their first game in Hungary on 4 June, one week after the Champions League final on 28 May, which itself is a week after the final round of Premier League fixtures on 22 May.
With European matches, EFL Cup semi-finals, the FA Cup fifth round and replays for earlier rounds, there are only two completely clear midweeks until the end of the season.
Those midweeks were supposed to be used for matches that had to be moved because teams had reached the latter stages of domestic cup competitions whose dates clashed with league games.