Reports emerged last night that Rangers had been issued with a letter from shareholders asking for a vote to remove Murray and fellow director Philip Cartmell.
The proposed resolution, if voted through, would put James Easdale and Chris Morgan on the board.
The club issued a statement to the London Stock Exchange on Thursday morning confirming that they were considering the request.
The statement read: "The board of Rangers has noted the recent press speculation regarding a requisition for a General Meeting.
"The board confirms that it has received such correspondence and is seeking to establish the validity of this requisition.
"Further announcements will be made as appropriate."