Gregg Wylde and Mervan Celik have become the first players to leave Rangers as part of the administration process.
The departures, reported by Sky News, are expected to be followed by at least three other.
Speaking earlier to STV, 20-year-old Wylde, who has made 47 appearances for the club, said: "I wanted to help out the club by keeping people in a job.
"I was so tired I couldn't really sleep at night.
"It was getting to me so I thought I would leave."
Further departures are likely with administrators Duff and Phelps expected to make redundancies after they failed to reach an agreement with the players on cost-cutting.
Celtic defender Charlie Mulgrew, who celebrated his 26th birthday today at the Hoops' Lennoxtown training ground picking up the Clydesdale Bank Premier League player of the month award for February, expressed sympathy for Wylde.
"I know one or two of them," said Mulgrew, who won his first cap for Scotland in the friendly in Slovenia.
"Somebody mentioned Gregg Wylde I know him and I know his family well.
"So I have a lot of sympathy towards him and I just hope things can get better over there.
"It just shows how good a character he is (to give up wages).
"Somebody was saying at lunch that he came through here (at Celtic) when he was 11.
"I am sure he will do okay and go on and get another club because he has done very well at Rangers and he is a very good player."
Talks broke up last night after players failed to reach agreement over wage cuts designed to save £1million a month.
Some players were reportedly asked to take pay cuts of 75% but the squad issued a counter-proposal, which Duff and Phelps considered overnight, aimed at preventing redundancies.
Joint administrator Paul Clark said last night: "Everyone involved in the administration process has been attempting to reach a consensual solution in regard to job losses within the playing squad.
"The prime reason for this has been to achieve essential cost savings while preserving the fabric of the first team.
"This has not been an easy balance to strike and we would like to thank the manager Ally McCoist, his players and the PFA Scotland for attempting to find a solution that would be workable for all. Every realistic option is being explored.
"Regrettably, it has not been possible thus far to reach a consensus where players could accept the necessary level of wage cuts to prevent job losses within the squad.
"We do not for a moment criticise the players for this as the wage reductions that would be required are very substantial and would have a significant impact on each individual.
"For clarity, we cannot enforce wage cuts. The players have to agree to this course of action.
"The players have asked us to consider a final proposal overnight for discussion in the morning and we have agreed to this request."
Duff and Phelps had previously set Monday as a deadline for a decision and said job losses were likely after refusing a request to allow wage deferrals.
However, former director Paul Murray, who has held talks with administrators over forming a takeover consortium, urged Duff and Phelps to consider deferrals as player redundancies would leave new owners with an expensive rebuilding job.
The financial dealings of Rangers face more scrutiny after the Scottish Premier League announced an inquiry into allegations that the club made undisclosed payments to players.
The SPL board instigated the investigation during a board meeting today following claims surrounding the club's use of employee benefit trusts (EBTs) during Sir David Murray's reign.
Former Rangers director Hugh Adam, who left the club in 2002, alleged that some payments were not included in official contracts that were registered with the SPL.
The use of EBTs, from 2001-2010, was the subject of a tax tribunal in January, which could result in a £49million bill, although Rangers have defended their use of the offshore payments.
But whether they were legal or not in the eyes of the tax tribunal would not matter if the club had not disclosed the payments on the official contracts.
A statement from the league read: "The SPL board has instructed an investigation into the alleged non-disclosure to the SPL of payments made by or on behalf of Rangers FC to players since 1 July 1998."
SPL rules prohibit payments to players that are not made "in accordance with a form of contract approved by the SPL".
Chief executive Neil Doncaster would not make any prediction on how long the investigation would take or which of 18 sanctions Rangers might face if found guilty.
Doncaster told Sky Sports News: "First we have to establish whether there were any payments that were made that were undisclosed at the time and, if they were, we will take that forward."
The Scottish Football Association confirmed on Friday they would investigate the allegations made by Adam.
The SFA had already launched an independent inquiry into recent events at Rangers after the club went into administration over unpaid tax bills last month, and specifically whether they broke rules regarding whether majority shareholder Craig Whyte was a "fit and proper" club official.
The SPL board meeting followed a general meeting where representatives from the 12 clubs discussed rules on financial fair play following Rangers' descent into administration.
Rangers were automatically deducted 10 points when they went into administration on February 14 but clubs today pondered whether the rules were fair and also the consequences should Rangers go into liquidation and emerge as a new company.
Dunfermline chairman John Yorkston said he would be uncomfortable with a 'newco' Rangers automatically taking their place in the SPL should the current club go into liquidation.
Yorkston told reporters: "As we speak today, if they come out of administration I personally feel it's a clean-slate job.
"If it's liquidation, it's a completely different kettle of fish.
"Liquidation is a completely different situation and they may well have to go down to the Third Division.
"We would have to look at it and see what all the facts are."
St Johnstone chairman Steve Brown would not address that specific issue but is a supporter of points deductions for clubs who are forced into insolvency scenarios.
"We try to run the club the proper way," Brown said.
"Other clubs have been allowed to refinance and I wouldn't say it annoys me, it's just unfortunately part of the game.
"We've run the club with no debt but unfortunately won no trophies, so until such times when you are rewarded for not going into debt then it's not going to change."
However, other SPL chairmen admitted they would consider the wider impact on Scottish football should a new Rangers emerge.
Kilmarnock chairman Michael Johnston said: "There are certainly commercial considerations at play here.
"There is no underestimating the value of Rangers and Celtic to the SPL and Scottish football in general so I think it would be foolish to overlook the commercial aspects of this for all the other clubs."
St Mirren chairman Stewart Gilmour said: "Scottish football needs a strong Rangers and Celtic, that's my personal view.
"But once we see what the whole position is, we as a club can make a decision from there.
"We try not to jump in off the cuff, I don't think it's the time for that. None of us really know what's happening with Rangers.
"It's a very difficult time for Rangers Football Club and the players and management. It's for their house to get sorted out.
"But I think in many ways it's better we all leave them to get sorted out, see where they are and then we can come to some decision."