A number of investors are keen for former director Paul Murray, accountancy expert Frank Blin and Sandy Easdale, brother of non-executive director James, to be appointed as directors.
The group have also proposed that former Rangers chairman John McClelland return to the board of the League One side.
The proposal was put to the club on September 4, with the shareholders signalling, if accepted, they were ready to withdraw a request for the removal of chief executive Craig Mather and other key directors.
Rangers are keen to avoid an EGM but have, as yet, failed to reach an agreement which would see the proposed boardroom changes on the agenda of next month's annual general meeting.
In a statement to the London Stock Exchange, the club said: "The Company confirms that while board discussions have continued with representatives of the group who requisitioned a general meeting to consider the proposed resolutions, the board is disappointed to announce no agreement has been reached.
"Unless an agreement can be reached prior to September 13, as set out in the announcement on September 2, the company will be required to send a notice to shareholders to convene the general meeting by no later than September 13.
"Further announcements will be made as appropriate."