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 the options.
Brentford boss Thomas Frank led calls for all matches to be called off until 26 December to enable a reset.
Some feel the break should be longer - but others such as Liverpool's Jurgen Klopp do not believe it should happen.
The Premier League said on Thursday it intends to carry on playing matches as long as it is safe to do so.
'We need clarity' - what clubs said on Friday
Arsenal boss Mikel Arteta: "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 need clarity."
Aston Villa boss Steven Gerrard: "We all want the same thing and want the game to continue. I don't have any concerns but I do have trust in the Premier League and the people who make the decisions.
"In terms of being in my shoes I have to prepare the team as best I can. We have had some cases in the playing staff and have had some cases in the staff.
"I'm hoping we have a good 24 hours or we could have a situation that grows and gets worse here."
Newcastle boss Eddie Howe: "I think it's probably on a knife edge would be my verdict on it.
"I think when you start losing players to Covid, I think then the worry for me is that the competition becomes slightly unfair. I don't think anyone wants to see that.
"The biggest thing people want to see is a fair league. They don't want to see disparity in games and players missing.
"We all want the product to continue, I'm desperate to continue the programme myself but I do think that the welfare of the players and supporters has to come first."
Liverpool boss Jurgen Klopp: "I'm not against stopping the league I just don't see the 100% benefit of it.
"Stopping it means stopping now for one or two weeks, so five or six games. When do you want to play them?
"Or we just play on. It is really difficult because step by step players will get infected."
Wolves boss Bruno Lage: "My family are coming [to games], so I am concerned about that.
"Sometimes we think about the professional life and forget about the other part. It is difficult to talk about Covid. We have to be aware it is not just about Covid but also the professional life."
Chelsea boss Thomas Tuchel: "It is not in my hands but clarity and transparency is always good in every subject.
"I know the rules now, I did not get involved too early. I read them and then immediately forgot them because there are so many of them."
Guardiola's inconclusive test result
Meanwhile Manchester City cancelled Friday's news conference with manager Pep Guardiola 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.
Manchester City's Women's Super League game with Reading, which was due to be played on Saturday, has also been postponed.
What about a potential fixture pile-up?
The meeting on Monday will not purely be centred around matches being called off and whether there is to be a break or not. There are also issues around re-arranging the games that have already been postponed.
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.
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.
What about the situation in the EFL?
With 18 fixtures in the English Football League postponed before the weekend, managers below the top flight have also been having their say.
In a statement on Thursday, the EFL said a quarter of players at its member clubs "do not intend to get a vaccine" against Covid-19.
Exeter City manager Matt Taylor told BBC Sport he would not be influencing any of his players to get vaccinated, stressing it was "their decision".
"From my discussions with players who haven't had the vaccine, there's a lot of influences, and they're understandable," Taylor said.
"Whether it be things in terms of enlarged organs, heart problems, respiratory problems, possible fertility issues, they've got a whole host of questions which come up and often remain unanswered.
"Sometimes people think it's a straightforward decision as to whether you do or don't get the vaccine. But it's not as easy a decision because everyone's circumstances are totally different."
Derby boss Wayne Rooney added: "It's a difficult situation because everyone has their own opinions on it.
"I've had the vaccinations but some players, some staff, might have their own personal opinions on it," he told BBC Radio Derby.
"I'd personally encourage it, we can see what's happening in terms of needing vaccinations to get into places, but also to stop it spreading and to make sure you're happy yourself and your family.
"I'd encourage it but I can't make that decision for all the players and staff, unfortunately."
What is the situation like in Europe?
More than 90% of La Liga players have been double vaccinated and stadiums are still allowed at full capacity.
A club cannot cancel a game as long as there are 30 available players registered between the first and second team.
The Spanish FA will announce a change to the protocol this Saturday, where players and staff will need "one antigen test a day and one PCR test every two weeks" according to Guillem Balague on the Euro Leagues podcast
Multiple Real Madrid players tested positive for coronavirus after an outbreak at their facilities - including Gareth Bale, Luka Modric and Marcelo.
In France, 95% of players have been double vaccinated and there are a low number of positive cases in Ligue 1.
There will be a two-week winter break beginning on 22 December, during much of which players will be away from training -in contrast to England, where games are being played every few days.
"The numbers of new positive cases in England are so high compared to the rest of Europe" said journalist Julien Laurens.
"In France we haven't had to cross that bridge yet because we haven't been in that position."
In the Bundesliga, 94% of players have been double vaccinated. However, top-flight games are limited to 50% attendance and are not allowed to exceed 15,000 supporters to minimise the risk of infection.
Bayern Munich's Joshua Kimmich tested positive for coronavirus in November after which he admitted he wished he had chosen to vaccinate earlier.
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