Rangers' administrators Duff and Phelps will give further consideration to three of the four bids submitted for the club yesterday.
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".
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."
Duff and Phelps have discussed alternative options with bidders in the event that a CVA is not possible, which could ultimately result in the club facing European and domestic football penalties.
Whitehouse added: "We would stress, however, that if a CVA could not be achieved, bidders have discussed with us the next best alternative being the sale of the business to a new legal entity which would continue to trade as Rangers Football Club.
"While such an arrangement is not desirable in so far as it would change the corporate entity, i.e. the registration number of the limited company, and would leave the club facing European and domestic football penalties, it nevertheless could provide a platform to enable new and substantial investment into the club to be made, which would in turn achieve the long term stability and viability of the business.
"As administrators, we would be in breach of our statutory duties if we rejected out of hand any legitimate proposal that asserted to secure the future of the club.
"This solution is not our primary objective nor our preferred option, however we would ask fans to understand that delivery of a CVA can only be achieved if purchasers are prepared to offer enough to provide a return to creditors at a commercially acceptable level. We do, however, believe this can be achieved.
"Our focus continues to be achieving the best solution for the club, its supporters and its creditors and we continue to believe this will be deliverable.
"We would expect to complete our negotiations in relation to the current round of bids, with the various stakeholders, including the major creditor groups over the next few days and we would hope that an announcement will be made during the course of next week with regard to the future ownership of the club.
"We are aware that some fans wish to stage a protest at the match on Saturday against any form of liquidation. We understand their deep concern on this issue but the bidding process is at a critical and sensitive stage and, as administrators, we cannot support action - even though we favour a CVA - that may be interpreted as ultimately detrimental to the club's prospects of emerging from the administration process successfully.
"The last few weeks have been extremely turbulent and a difficult time for the football club and I would like to thank the fans, the players and all of the staff at the club for their tremendous continued support throughout this period."