Rangers confirmed on Wednesday they would consider a request to add former chairman John McClelland and three other men to their board of directors.
A group of disgruntled investors led by billionaire businessman Jim McColl also proposed appointing former director Paul Murray, Sandy Easdale - the brother of current non-executive director James - and accountancy expert Frank Blin as directors.
Mr McColl, chairman of Clyde Blowers, and his group had previously called for an extraordinary general meeting in a bid to have chief executive Craig Mather, finance director Brian Stockbridge and director Bryan Smart removed from the board.
But it appeared they had signalled their intention to withdraw that request in the event that the quartet, led by McClelland, were admitted to the board.
However, the group has now stated that shareholders deserve the right to vote on the re-election of any director.
In a statement issued to the Stock Exchange on Wednesday, the club said: "The board considers that any decision on any proposal for the withdrawal of the requisition would be subject to the provision by the requisitioners of a vote of confidence and continued support for the current directors and to all necessary regulatory approvals."
However, a subsequent statement on behalf of McColl's group said: "On behalf of the requisitionists we have made it clear to the Rangers board that we are proposing the additions to the board now to enable it to operate more effectively as a balanced unit in the run-up to the AGM in October.
"We have also made it clear that all directors, both existing and new, have to offer themselves up for re-election at a vote at the AGM. We believe this is fair and gives all shareholders the opportunity of voting for who they want on the board.
"We agreed this position with the board and were therefore surprised to see the statement issued by the club which seemed to suggest that any agreement was conditional on a 'vote of confidence' in the current board members now and on a continuing basis.
"This is contrary to our understanding of the agreement we had with the board."