Duff and Phelps last night set a 48-hour deadline over the sale of the club after cost-cutting talks involving slashing players' salaries to prevent redundancies broke down.
The administrators are already considering the possibility of liquidation if they cannot reach a deal and have discussed with the Scottish Football Association the implications if a new company (newco) took over Rangers' assets, which include Ibrox and Murray Park.
The insolvency firm warned that, without a sale, the scale of the cost-cutting it envisaged might deter would-be buyers.
They also said Rangers may not be able to fulfil their remaining SPL fixtures without the promise of new income or drastic measures to reduce costs.
The moves came despite serious concerns that issues materially affecting a sale of Rangers have not been resolved. These include the validity of owner Craig Whyte's position as preferred creditor with first claim on the assets of Rangers, which many believe cannot be resolved without a legal battle.
Whyte is expected to fight any attempt to prise away his hold over assets, even though he admitted using more than £20 million of supporters' season ticket money to help complete his £1 takeover of Rangers in May last year.
The administrators' warning came after they were unable to agree measures to cut costs, which included wage cuts, with the playing staff on terms "that will preserve value in the business".
David Whitehouse, joint administrator, said: "The club is in a perilous financial situation and that should not be under-estimated.
"In the next 48 hours or so we are approaching and meeting with those parties who have already expressed an interest in acquiring the club to try to accelerate what would be a normal timetable for this sort of transaction.
"We have to look at the time constraint and if it is possible to conclude a transaction within a very short timetable, simply because we can't deliver the cost cuts necessary to keep the fabric of the business in place, then we would also have to look at selling into a newco scenario."
Rangers' second-biggest shareholder, Dave King, who is backing former director Paul Murray's Blue Knights consortium bid, issued a statement earlier yesterday saying it was "inevitable" the club would be liquidated. His assessment came as he announced his intention to sue the club's former owner Sir David Murray for £20m.
In his statement, Mr Whitehouse stressed that in liquidation they would "still envisage that Rangers Football Club could play football and operate as a football team".
"We have always said that liquidation is a possible scenario," he added. "The preferred scenario from our perspective, both in terms of the return to creditors and a platform for retaining an ongoing continuous business, is through a company voluntary arrangement.
"No-one should be in any doubt that, in the absence of sufficient cost-cutting measures or receipt of substantial unplanned income, the club will not be able to fulfil its fixtures throughout the remainder of the season."
Mr Whitehouse said that if a sale cannot be accelerated, then "we will have to either secure cost-cuts with the consent of the players or make some quite serious and deep redundancies".
Mr Murray, who intends to make a conditional offer to the club's administrators before an initial March 16 deadline, told The Herald that Whyte's hold on Rangers' assets was "one of the questions the administrator has to answer to put the club into a sellable form".
He warned that making significant cuts to the squad would leave Rangers less attractive to buyers as it could cost £20m to replace the lost players.
Asked if Rangers was in a state to be sold, an administrators source admitted: "There's an awful lot still to be resolved.
"It is all about who owns what. It doesn't matter whether you are selling a house, or a football club, or a company, you have to know what you're buying."
The administrators made their stark warning over the club's future while confirming Rangers had no chance of competing in Europe next season as they would not be able to submit fully audited accounts by a March 31 deadline.
South Africa-based Mr King, who was born and raised in Castlemilk, Glasgow, and is the only survivor from the Sir David Murray era on the board, hit out at the past and present owners for an alleged lack of clarity over the club's true financial state.
Mr King said he was going to sue Sir David for £20m on the basis of "non-disclosure". The Murray Group responded with a statement that read: "We note with some interest, and much incredulity, Dave King's press statement."
Mr King also expressed frustration over financial information given to him by Whyte, who he accused of "duping" fans over the funding of his takeover.
Meanwhile, Whyte said there was "absolutely no necessity for Rangers Football Club to go into liquidation".
He added: "I believe we will come out of administration by way of a creditors voluntary agreement. That is in the interests of all the stockholders."