Brighton's chief executive, technical director and head coach have all taken a pay cut for the next three months.
Former England captain Gary Lineker predicts that many Premier League players will now follow suit.
Clubs have been criticised by British politicians for furloughing non-playing staff while paying players in full.
MP Julian Knight has called for the Chancellor to impose a "windfall tax" on clubs that refuse to cut players' salaries while furloughing staff.
In a letter to Chancellor Rishi Sunak on Thursday, Knight, who is chair of the Digital, Culture, Media and Sport committee, suggested a deadline of 7 April for clubs to take action or be sanctioned.
"If the Premier League isn't going to act to resolve this crisis then the government must step in by imposing a significant financial penalty on clubs to reimburse those hit hardest in the pocket," said Knight.
Bournemouth manager Eddie Howe became the first Premier League boss to take a voluntary pay cut during the ongoing coronavirus pandemic on Wednesday.
Brighton chief executive Paul Barber said: "It is entirely appropriate that we play a very small part in reducing the financial burden."
Barber, technical director Dan Ashworth and head coach Graham Potter have each taken a "significant" voluntary pay cut but no decision has been taken on whether to furlough any of the club's staff.
"We have seen our income literally disappear overnight," added Barber.
Players, coaches and executive staff at Norwich have donated £200,000, made up of a percentage of their salaries, to help local people affected by the pandemic.
Players at Championship leaders Leeds United have already volunteered to take a wage deferral while Birmingham City players who earn more than £6,000 a week have been asked to take a 50% cut for the next four months.
In Europe, Barcelona and Atletico Madrid players have taken a 70% pay cut while Juventus players and manager Maurizio Sarri have agreed to freeze their pay for four months.
'Football will, and should, do something'
BBC Match of the Day presenter and former England skipper Lineker expects many top-flight players to take pay cuts but also defended them from criticism, calling players "easy targets" and asking for patience.
However, Lineker - who is donating two months of his BBC salary to the British Red Cross - criticised his former club Tottenham for furloughing staff.
"People do focus on footballers, they are an easy target," he told BBC Radio 4's World at One.
"There are lots of other people in society who earn huge money - billionaires, CEOs on huge money - I hope it’s not just footballers who are targeted. Football will, and should, do something.
"My inkling is that players will take pay cuts, they will help out, they will make donations in whatever way they can help.
"The way Tottenham have handled it has not been very good, what they are doing to their staff, I don’t agree with whatsoever. But that is a separate issue to what players do.
"We are two to three weeks behind Italy and Spain in the scheme of things and players there in recent days have have taken cuts.
"I strongly suspect the same thing will happen here, footballers do an amazing amount of great work in the community and I’m sure they’ll want to stand up at this moment."