Financial firm Duff and Phelps were called in last Tuesday over an unpaid tax bill accrued since Craig Whyte's takeover of the Scottish champions last May.
They have praised the continued support of fans, business partners and sponsors - as well as the Scottish Premier League and the Scottish Football Association - as they work towards securing the club's survival.
David Whitehouse, joint administrator, said in a statement on Wednesday night: "Overall, I would describe the situation as positive. Everybody recognises the plight that the club is in and have come to the table to help and assist where possible.
"We have also had very good support from the football authorities and have met with both the SFA and the SPL.
"For 140 years Rangers has been a key part of Scottish football. We hope that the influence and the support which the club has given to the game over the years will carry some weight at these difficult times.
"Generally other clubs are sympathetic. I think clubs realise this is a difficult time for the football industry in general and Rangers isn't unique in its financial position.
"They are very supportive of the survival of the club which is critical to Scottish football."
Rangers attracted their biggest home crowd of the season for last week's Scottish Premier League game against Kilmarnock at Ibrox - their first match since going into administration.
Whitehouse told supporters that further backing from them is crucial in generating income and helping to secure the club's future.
He added: "The Rangers fans have been absolutely tremendous over the last 10 days and it's vital to the administration process that we continue to receive the support we have had thus far.
"Ibrox was sold out last Saturday and hopefully that can be the case for the rest of the season.
"The fans are clearly extremely loyal to Rangers and by coming to matches at Ibrox they are directly contributing to the club's future.
"We are hopeful that we can enhance revenue streams in the coming months through a variety of means and we have been very encouraged by the support of the business partners who have helped in that regard already.
"The club's suppliers are also working with us to improve income flows where possible and the sponsors have also been tremendously supportive.
"We are in discussion with them to see if we can enhance the packages that we currently have in place.
"This is obviously a very difficult period for the club but those who come to the fore and support the club will obtain tremendous publicity which is what sponsorship is all about.
"Right now, it is quite simple - income now will help secure the future of Rangers.
"Our focus is on generating income for the club but there is also a focus on costs and the steps we are taking in terms of the cost base of the club will evolve during the next week.
"On a daily basis we are talking to department heads and seeing where there is capacity for cost savings but being very mindful of the need both to preserve the performance on the pitch and retain the efficiency of the club off the pitch as well."
Meanwhile, it is understood the SPL are looking into the match delegate's report in relation to alleged unacceptable conduct by Rangers fans during the 1-0 defeat to Kilmarnock last week.
On Wednesday night, former Rangers chairman Alastair Johnston questioned whether Whyte met the conditions of the sale purchase agreement when he purchased Sir David Murray's majority shareholding.
On Tuesday, the administrators and Whyte himself confirmed that a £24million cash injection from investment firm Ticketus, based on advance season tickets sales, had been used to pay off the £18million debt owed to Lloyds Banking Group as part of the takeover.
In a letter sent to administrators Duff and Phelps on Wednesday - and published on STV's website on Wednesday night - Johnston said: "As the former Chairman of Rangers Football Club who acted in such a capacity during the period surrounding the acquisition of the majority shareholding in the Club by Wavetower Limited, I would request that you investigate and report on the issues pertaining to compliance with Part III, paragraph 1 of the 'Circular to the Shareholders of The Rangers Football Club P.L.C.', dated June 3, 2011, a copy of which has been previously furnished to you.
"The Purchaser's Warranties and Undertakings recited in this paragraph are self-explanatory and 'are expressed to be enforceable by both the Club and Vendor'.
"In this regard, I draw your attention to the recourse described in Para 1 (h), i.e. 'A breach of any undertakings given by the Rangers FC Group in the agreement will result in the debt acquired being automatically extinguished'.
"This issue has apparently also been of concern to the vendor because Sir David Murray issued a public statement on February 14 which included the following comment, 'MIH wrote to Wavetower on 25 August 2011 seeking confirmation that its various obligations were being complied with. A confirmatory assurance was eventually obtained on January 3, 2012. Following recent speculation concerning the financing and security arrangements put in place by Wavetower, a request was issued seeking further clarity'.
"As you know, the status of the Club at this time is precarious, but efforts involving investors and/or supporters are being developed to initiate and execute a recovery to self-standing sustainability.
"Wavetower's (Craig Whyte's) leverage during this process is a function of his purported position as the primary secured creditor by dint of the £18million loan which he claims he has provided to the Club on an unencumbered basis.
"If, however, this entitlement cannot be sustained based on any breach as referred to above thus precipitating the extinction of the loan in question, then the options for charting a course for reconstitution of Rangers Football Club will be much more readily identifiable.
"I, therefore, believe that it would serve the public interest for the Administrators to make a full declaration with respect to relevant compliance."
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