The auditors said uncertainty over the funds could harm the company's ability to continue trading, while directors warned that the move could "destabilise and damage the club".
Last night Rangers chief executive Graham Wallace appealed for breathing space and help from fans to put the club's finances back on track. He said: "I have a very clear idea of what we need to do. We are heading in the right direction but we need time."
The Union of Fans, which incorporates all fan groups, called for supporters to withhold season ticket money and put it into a trust until club assets including Ibrox Stadium and Murray Park training ground were signed over to them as collateral, to ensure they are protected.
Their move came after a meeting with former Rangers director Dave King, who has revealed plans to invest as much as £30 million of his own cash.
But in the report of Rangers International Football Club (RIFC) plc's interm results, auditors Deloitte say issues over the timing of receipt of season ticket money indicated the existence of a "material uncertainty [that]may cast significant doubt about the company's ability to continue as a going concern".
Notes in the results report relating to "going concern" issues add: "The directors are aware of recent public comment suggesting fans defer, withhold or ring-fence their season ticket monies.
"These comments are particularly unhelpful as they have the potential to destabilise and damage the club. If this were to happen, it would force the club to operate in a manner different from every other football club, where the receipt of season ticket monies in advance of games taking place is an established and accepted part of the normal working capital cycle."
Rangers chairman David Somers said the suggestion season ticket money could be diverted created a "material uncertainty which may cast doubt" over RIFC plc's ability to continue as a going concern.
A Union of Fans spokesman said criticism directed at fans was "absurd" and said the board could resolve any issues surrounding the withholding of season ticket cash by handing over the security of club assets to them to ensure they are protected from any future fundraising efforts.
He said: "It is a pretty extraordinary statement when you consider what the fans have done over the last two years, putting in millions. It is quite a simple thing to accept the demands and give the security across, and they will get the season ticket money in a lump sum.
"Nobody has a wish to withhold it but, in the absence of any transparency over what their plans are or any evidence they have the cash situation under control, it would be slightly foolhardy for everyone to pile their season ticket money in again. We have seen in the past few years it has been effectively squandered. What we don't accept is that the fans would somehow be to blame for not putting that money in and affecting the club."
Mr King, who met with boardroom representatives more than two weeks ago, said the board confirmed the assets would not be used as security and added "no-one should be in any doubt this public statement and commitment is significant and should be appreciated as such".
Mr Wallace felt the half-year results to December 31, 2013, which showed a loss of £3.7m in the six months up to the end of 2013, an improvement of 50% on the seven-month period 12 months earlier, were a "step forward".
In a full interview, he described Rangers fans as "tremendously loyal" and added: "I think they can see we are making progress."
He added: "The most important thing to them is that the [company] does not go into administration again. The huge cost base and cash burn has gone and we are managing the costs, but there will be no slash and burn. As far as the wages are concerned we have to be competitive and on the football side we will always need to have a significant player bill."
In their latest figures, Rangers announced their cash reserves had fallen £17.5m to £3.5m for the year ending December 31, 2013, despite bringing in £22m in their initial public offering a year earlier.
Revenue was up by 38% to £13.2m from £9.5m, operating expenses remained almost identical at £16.8m from £16.6m while staff costs were down £800,000 to £7.5m with £500,000 of that spent on severance payments.
The club made assumptions, including that they "modestly" increase their season-ticket numbers, which stood at 36,000 in League One, next season and beyond.
Mr Somers recognised the support of the fans, but raised further "significant concern that external comment and ill-informed opinion continues to create uncertainty with regard to future income and cash flows".
He added: "Nevertheless, after making the appropriate inquiries and considering the uncertainties referred to above, the directors have concluded there is a reasonable expectation the company has adequate resources to continue in operational existence for the foreseeable future."