Rangers' administrators Duff and Phelps will give further consideration to three of the four bids submitted for the club which is believed to be £134 million in debt.
As well as a bid from the Blue Knights and Ticketus, it is believed other offers lodged before the 5pm deadline were from groups based in Germany, Singapore and the United States.
Administrators have now indicated they are no longer considering one of those proposals, while reiterating their belief that an exit from administration before the end of the season is "achievable".
Latest reports from the BBC state that Rangers' administrators estimate that the club's total debts could top £134m.
David Whitehouse, joint administrator, said: "Following the outcome of the bidding process, I can confirm today that we will be considering further three of the four bids submitted yesterday."
Administrators believe the most likely exit from administration will be via a Company Voluntary Arrangement (CVA), despite recent speculation the company could be liquidated.
Whitehouse said:"We have had a number of discussions with the interested parties today and have stressed the benefits to them of engaging openly with the club's fanbase.
"We can now see light at the end of the tunnel whereby the club can exit from administration and focus upon success on the pitch.
"While we cannot be precise on timescale, exit from administration does look achievable by the end of the season.
"We also hope to announce next week acceptance of one bid, which would then be subject to a period of due diligence and exclusivity.
"Most importantly, following the bidding process, we believe that the most likely exit from administration will be the successful implementation of a CVA.
"Much has been speculated over recent weeks about the form of exit which the club will take from administration.
"This is an extremely complicated case, not least because of the requirements to meet insolvency legislation, the rules of the various football authorities and the contractual requirements of key business partners of the club.
"It is, however, appropriate that we once again set out our position in relation to the manner in which we are seeking to achieve an exit from administration.
"The first objective of administration is to achieve the survival of the company as a going concern. In relation to the football club this can only be achieved via the exit from administration through a CVA.
"A CVA is a process by which creditors are presented with a proposal to deal with the legacy debts of the company.
"Creditors in turn vote upon those proposals and therefore there is a requirement for a CVA to meet the commercial needs of creditors.
"It is, therefore, essential that any CVA proposal is commercially acceptable to the general body of creditors.
"The ability of the company to exit through a CVA process is, therefore, dependent in part, on the level of offers submitted for the business and is in the gift of the potential purchasers to deliver.
"As stated, we believe this can be achieved.''