Manchester City manager Pep Guardiola raised the possibility of players going on strike over their welfare – then said there was “no reason” to do so and he does not think it will happen.
Premier League clubs chose to fulfil festive fixtures at a meeting on Monday despite a rise in Covid-19 cases.
Guardiola said a strike may be the only way to get the authorities to listen.
Speaking on Thursday, he said: “Should the players and the managers be all together and make a strike, or something, because just through words it’s not going to be solved?”
But asked if things could come to a strike, he added: “No, I don’t think so because we want to play. We want to continue – to make the people happy going to the stadium on the 26th, 27th, 29th, 31st and 1st, and play games, because we love to do that.
“I’m not saying there’s a reason to make a strike.”
Premier League players and club staff returned a record 90 positive Covid-19 tests last week, and six of last weekend’s 10 fixtures were postponed.
Two of the matches due to take place on 26 December – Liverpool v Leeds and Wolves v Watford – have since been postponed, and Everton manager Rafael Benitez said he could not understand why his side’s match will still take place.
In an interview with BBC Sport, Liverpool captain Henderson said: “I don’t think people can appreciate how intense it is until you actually see it first hand.
“Football to us is everything and we want to be able to perform at the highest level every time we set foot on the pitch. And unfortunately, in this period it is difficult to do that.
“We will try to have conversations in the background and try to have some sort of influence going forward, but at the minute I don’t feel the players get the respect they deserve in terms of having somebody being able to speak for them independently and having the power to say actually this isn’t right for player welfare.”
Liverpool assistant manager Pep Lijnders said on Tuesday the schedule was “absurd”, while Chelsea boss Thomas Tuchel said he is having to take “huge risks” with his players’ fitness.