Jurgen Klopp said Tuesday he was unsure whether closing stadiums would help tackle the coronavirus as Pep Guardiola admitted he did not like the idea of matches being played in empty stadiums.
No restrictions have yet been placed on games played in Britain and Liverpool will host Atletico Madrid on Wednesday in front of a capacity crowd of more than 50,000.
Nearly 3,000 Atletico fans are expected to travel for the game even though La Liga has announced that all matches in Spain will be played behind closed doors for the next two weeks.
"Some things are more important than football, we realise that in this moment," Liverpool boss Klopp said ahead of his side's Champions League last-16, second-leg match.
"I don't know enough about how much it would help with the football games. The problem with football games is if you are not at the stadium you are in closed rooms watching, maybe together. I'm not sure what is better in this case."
Liverpool are expected to wrap up a first English league title in 30 years in the coming weeks but could do so in an empty stadium if authorities tighten the rules.
The Champions League has been severely disrupted by the fast-spreading virus.
Paris Saint-Germain and Barcelona will play their second-leg matches behind closed doors, while it remains to be seen if Juventus can host Lyon next week with Italy in lockdown.
Manchester City boss Guardiola believes it is only a matter of time before English clubs face further restrictions.
City play Arsenal at home on Wednesday in a re-arranged Premier League game - when Guardiola will go head to head with his former assistant, Mikel Arteta.
Guardiola, whose side are due to host Real Madrid in the Champions League next week, does not want a prolonged period of games without fans.
"We are here for the people. If it's just one or two games, OK, but not longer," he said. "We play for them and if they cannot be there, then there is no sense. I wouldn't love it.
"But if (European governing body) UEFA or the government say we have to play without spectators, we will do it. The health is the most important thing and we have to take care of the situation."
Wolves boss Nuno Espirito Santo, whose side are due to face Olympiakos in the Europa League on Thursday in an empty stadium in Greece, said football should stop instead of being played behind closed doors.
"If we have to go we will. But we don't agree - we're not happy to go," he told Sky Sports.
"Behind closed doors doesn't make sense," he added. We're pretending to live a normal life when things aren't normal."
On the pitch, Klopp is focused on overturning a 1-0 first-leg deficit against Atletico to maintain his record of never losing a two-legged European tie in five years as Liverpool boss.
Diego Simeone's side frustrated the Reds in Spain three weeks ago and Klopp demanded a higher tempo from his side to unsettle Atletico's famously well-organised defence.
"If you play predictable, Atletico defends you for the next six months without a rest," said Klopp.
"It is really good what they are doing, (I have the) highest respect, but there are ways and we have to find them tomorrow night."
Simeone is looking forward to his first taste of Anfield and believes it would have be unfair on Liverpool to play the game behind closed doors.
"I have not played as a player or a coach (here). I haven't had the chance to play in what is marvellous stadium," said the Argentine.
"I hope they play the game with fans because it would not be fair on Liverpool to have played in our stadium with the importance of the impact our fans made and this time be missing their fans."