The Rangers board and a group of disgruntled shareholders have failed to reach a compromise on demands for change following several rounds of talks.
But they are close to agreeing a deal to postpone a vote until the AGM, rather than call a special general meeting.
Earlier this month, a group including Clyde Blowers chairman Jim McColl requested the appointment of Frank Blin and Paul Murray along with the removal of Brian Stockbridge, Bryan Smart and chief executive Craig Mather from the board.
In a statement to the London Stock Exchange, the Rangers board said it had been in "continual discussions" with the requisitioners.
The statement added: "One of the aims of these discussions has been to avoid the need for a general meeting, at this time, and the associated unnecessary cost and disruption to the company of convening two meetings, a general meeting and then the company's annual general meeting, which is expected to be held in October 2013, in short succession.
"The board has secured the written commitment from the requisitioners that they accept the validity and logic of this view and the company and the requisitioners are now exploring the mechanics of rolling the business of the general meeting into the business of the annual general meeting, on the understanding that an agreement will be reached on the terms upon which this will be done, by the close of business on August 27, 2013.
"Failing such agreement being reached by this time, the board will be required to send notice to shareholders to convene the general meeting by no later than August 30, 2013."
McColl soon released a statement accepting the logic of a combined meeting. But he continued to call on the board to accept the proposals for change, which were backed by Walter Smith when he quit as chairman and have been endorsed by supporters' groups.
McColl said: "Over the last couple of days we have been approached by members of the Rangers board seeking to explore whether there may be scope for a negotiation on the composition of the Rangers board which would avoid the need for a general meeting.
"These discussions were conducted in good faith but unfortunately the board was unable to deliver the changes sought by the shareholders who have requisitioned the general meeting.
"We are aware that the company is due to have its first AGM in October and so, in the interests of saving the club expense and time, we have discussed with the board a proposal to combine proceedings with the resolutions we sought as part of a general meeting being followed by the 'normal' business of the AGM.
"To allow time to deal with the mechanics of combining the resolutions which would otherwise have come up at two separate meetings, we have agreed to give the company until close of business on Tuesday 27 August to agree the terms of the legal paperwork.
"In the meantime we would encourage the board to make the changes that we believe are being demanded by the majority of stakeholders in the club."
- Investment & Company Information