Newcastle boss Steve Bruce questioned the morality of playing football during the worsening coronavirus pandemic on Friday while Aston Villa prepared to field a second-string team against Liverpool in the FA Cup.
There are growing concerns over whether the Premier League season can be completed on time as a new variant of Covid-19 sweeps across Britain.
A record-high 40 positive tests were detected among top-flight players and staff in the week between December 28 and January 3 and four Premier League games have already been postponed.
The English Football League, which oversees the three divisions below the Premier League, reported 112 positive tests on Friday.
The resurgent virus has wreaked havoc with scheduling at all levels of the English game but Premier League bosses have remained adamant that the season will proceed.
Newcastle were the first Premier League team this season forced to postpone a match this season, when they asked for their match against Aston Villa on December 4 to be deferred.
Bruce questioned the morality of playing on as the pandemic tightens its grip.
"The speed which it hit our club within a week, and ripped through, is something which all clubs will be looking at now," he said.
"It's difficult to contain and it leaves people sick. Financially it's right to play on but morally, for me, it's probably wrong."
Leeds boss Marcelo Bielsa agreed there was a moral argument for suspending elite-level football.
But Manchester United manager Ole Gunnar Solskjaer said football should continue despite the "frightening" situation.
"Of course what's happening outside and at different clubs and in the society is frightening and we have a responsibility and a duty to try to do our best to stay clear and keep within the bubbles and the guidelines," he said.
"I hope that we can continue playing because I think it's a positive impact for everyone in the lockdown now to watch."
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Aston Villa's FA Cup third-round clash with Liverpool on Friday is set to go ahead even though a large number of players at the Midlands club tested positive for coronavirus.
Villa will field a line-up featuring under-23 and under-18 players, but there are serious questions over their ability to fulfil the Premier League fixture against Tottenham next Wednesday and the following weekend's game against Everton.
Spurs already face a punishing schedule due to European and other commitments plus the postponement of their recent match against Fulham, who suffered their own Covid outbreak.
Spurs boss Jose Mourinho said it would be "completely impossible" for any more of his side's Premier League matches to be postponed.
Top-flight clubs were emailed details of tightened protocols on Thursday. These include allowing Covid compliance officers access to dressing rooms and making it mandatory for substitutes to wear face coverings when sitting n the stands.
League bosses know they are walking a tightrope in terms of the fixture list, with the rescheduled Euro 2020 due to start in June.
Burnley boss Sean Dyche believes footballers should be vaccinated to prevent the season being halted.
"The amount of money being spent on testing in the Premier League, if that money was channelled back into the NHS and the vaccinations system, surely that's a better place to be than it is just continuing testing a load of footballers two, three, four times a week," he said.
Southampton's FA Cup match against Shrewsbury is off after a Covid-19 outbreak at the League One club.
Brentford will host fellow Championship side Middlesbrough in the FA Cup without manager Thomas Frank in the dugout after he tested positive for Covid, while Middlesbrough's preparations were disrupted by a series of positive tests.
Wayne Rooney's Derby will field a youth team in their cup tie against Chorley.