Mr Hancock has led calls for Premier League players to accept salary reductions amid the crisis, calling for them to "play their part” in the national effort against Covid-19.
Over the weekend, Mr Hancock - who has been invited by Gary Neville to debate the topic on Sky's Monday Night Football programme - then suggested that players should donate a part of their wages to struggling hospices.
"I've seen that some, for instance footballers, are now making significant donations to charities and I really welcome that, that's exactly what we need to see," he told ITV News.
"But instead of having a row about this I think that people should come together and make a contribution.
"The hospices of this country have traditionally been largely funded by charity and charity shops.
"Those shops have had to close so I'm putting more money - taxpayer's money - into hospices to support them but why don't our footballers club together and support our hospices and support the national effort that we're all in?
"I think that is the sort of thing that would go down really well and help bring the country together."
Mr Hancock's comments have drawn an angry reaction from plenty of current and former footballers such as Wayne Rooney, Gary Lineker and Neville, who feel as if players are being made into scapegoats during the crisis and already doing a lot to help.
And Taylor - in charge of the PFA since 1981 - has now relayed his own shock at the Health Secretary's comments.
Taylor told Telegraph Sport: "I found it astonishing that Matt Hancock could come out like that when he's got his own issues with trying to get the necessary protective health equipment for our NHS workers and didn't have the tests in place either."
The PFA joined the Premier League, League Managers Association (LMA) and representatives from all clubs on a conference call on Saturday, subsequently warning that the proposed 30 per cent salary cuts for Premier League players - which they said would equate to over £500million over a 12-month period - would be detrimental to the NHS and cost the government £200m in tax contributions.
The PFA also welcomed the Premier League's decision to donate £20m to the NHS, but believe that sum could be "far bigger".
Talks will continue this week and Taylor has implored clubs to give the detailed financial information they had been expecting in order to make sure money goes to the right places.
"I think if they can't do that and explain the position fully then they have every right to expect players to mistrust what is happening," he said.
Asked if players were concerned about where the money would go, Taylor said: "Exactly that. They want the complete due diligence. They're not stupid.
"They've not just got their brains in their feet. They want to know the reasons for it and where it's going."
Additional reporting by the Press Association.