The Gers board met yesterday to discuss the group's requisition for a general meeting.
The institutional investors, who are backed by Scottish businessman and shareholder Jim McColl want three directors removed.
They have called for chief executive Craig Mather, non- executive director Bryan Smart and financial director Brian Stockbridge to leave.
They then would like ex-director Paul Murray and Frank Blin, former executive chairman of accountants PriceWaterhouseCoopers, appointed in their place. The existing board last night revealed in a statement that they are prepared to accept Blin becoming a director.
However, the prospect of Murray, who served
on the oldco board and fronted the Blue Knights' unsuccessful bid to take over last summer, returning has not been welcomed.
The statement read: "The directors remain hopeful that compromise can be reached."
But the group of shareholders, who believe they have the necessary
backing to push through change, look certain to reject the offer to bring Blin onto the board.
The three main
supporters groups, the Assembly, the Association and the Trust, have said they will back the move to replace the three directors.
And they have urged their fellow Light Blues fans to do the same.
That would mean the general meeting would go ahead next month as proposed.
The statement read: "The directors can state categorically that they have always been open to adding to the current size of the Board and are actively seeking
a new chairman, one who will bring instant and significant benefits.
"In particular it will
be necessary to connect strongly with corporate Britain if the board's
ambitions for Rangers are to be fulfilled.
"This board has been working tirelessly to find an intelligent solution to the request for a general meeting and all of the
directors are open to
sensible and reasonable additions.
"For instance, the board are not against Frank Blin becoming a Director but do have
reservations about other proposals.
"Even so, the directors remain hopeful compromise can be reached and that everyone, the fans especially, will see this Club emerge a much more stable and vibrant operation.
"It is the board's belief that with the right level of understanding from all sides Rangers will prosper and be stronger than at any time in its history.
"This is what the directors are committed to achieving through the work of an enhanced
but perfectly-balanced board."
As was reported in later editions of the Evening Times yesterday, the board decided to terminate the consultancy agreement with controversial former chief
executive Charles Green with immediate effect.
Green angered McCoist with his public comments after making a surprise return to the club earlier this month and Walter Smith resigned as
chairman just days afterwards.
The Yorkshire businessman had stood down as chief executive back in April after making allegedly racist comments.
He also departed the club after it was claimed that he had links with former owner Craig Whyte and details of how his takeover of the club were conducted.
An internal probe was conducted into the claims and Green was not found to have any existing connection to Whyte.
The three Rangers fans groups called for him to leave the club in a joint statement on Monday.