The demand came from Alex Wilson, one of the gang of four requisitioners who failed in a bid to be voted onto the club board.
And he hit out at the board for a "cack-handed" failure to lead by example after the players rejected pleas to take a 15% pay cut for the next season and a half.
He said: "I was appalled, surprised and disappointed that the players were asked to consider a 15% pay cut in isolation. It was a bit cack-handed.
"Ally McCoist has agreed to a reduction in his salary.
"But apart from that, I haven't heard of any other cost-cutting measures from the board other than this one.
"Sorry, but that is just not the right way to go about it. I was pleased to see the manager has backed the stance of his players."
Gers chief executive Graham Wallace has warned every area of the business, which is operating at a significant monthly loss, is currently under review.
And he has promised that each department of the SPFL League One club would be subjected to exactly the same scrutiny.
Wilson and his fellow requisitioners Scott Murdoch, Malcolm Murray and Paul Murray, had vowed to work for free if they were elected to the board.
And the lifelong fan and current season ticket holder, who was HR director at telecommunications giants BT for nine years, has called for directors to be proactive. "As requisitioners, we said we would work for nothing for an indefinite period if we were elected to the board.
"I would like to see the current board do the same thing.
"I would like to see them lead by example here by accepting reductions in their pay and agreeing to forego any bonuses they have in their contracts or fees which they are entitled to.
"They could lead by example by doing that for the next one or two years - or even until Rangers return to European football."
Wilson added: "You don't ask your troops to make sacrifices without making any yourself. Leaders should be leading by example.
"They can show to supporters that they are the sort of people who want to see Rangers flourish by making significant degrees of self-sacrifice here."
Wilson, who commutes from London to attend Rangers home games, fears that offering the players a pay cut will create unrest within the Ibrox club.
He said: "The club could have gone to the players and said: 'We have agreed to a pay cut and not to take any bonuses - we would like you to consider giving up 15% of your salary for a year.
"They could have presented it as a package. But to lead with your chin, even speculatively, was very cack-handed.
"The board, the manager, the backroom staff, the playing staff should all be treated the same way so they have got a unified structure.
"Doing it the way they have only creates disunity."