Former Rangers oldco director Murray, former Light Blues chairman Malcolm Murray - plus allies Scott Murdoch and Alex Wilson - known as the requisitioners, are seeking a place on the board.
The Ibrox club's five current PLC directors - chairman David Somers, chief executive Graham Wallace, James Easdale, Norman Crighton and finance director Brian Stockbridge - all face a re-election vote with reports on Tuesday night claiming that they have won the backing of a majority of shareholders which would keep them in situ.
Murray was quoted as saying: "The only two groups privy to this information would be Capita (who will verify the poll) or the Rangers board. If either of those parties have indeed leaked this data then it is an extremely serious matter."
A spokesman for Rangers said: "The board have noted with great concern statements made by requistioner Paul Murray over media stories speculating about the votes cast for Thursday's AGM.
"We feel this is an attack on the integrity of board members.
"The board are dismayed that an experienced businessman with knowledge of city practises could suggest that our board would leak information to the media before the AGM.
"In point of fact, the board did not have the final voting figures and therefore it would have been physically impossible to leak anything.
"We deplore the latest tactic of Mr Murray's which can only serve to inflame supporters and would ask him to take the honourable course and withdraw his accusation."
Capita have also released a statement to Sky Sports News which read: "Capita Registrars provides support services for shareholder meetings, including the collation and analysis of votes, to more than 1300 companies and observes the highest standards of confidentiality and integrity as a matter of course.
"We have, nonetheless, conducted a detailed investigation into the circumstances surrounding the alleged leak of information surrounding the Rangers International Football Club plc AGM vote and are confident that all necessary protocols were rigorously adhered to and that no information was shared inappropriately."
The AGM will get under way at around 10.30am on Thursday - the first at Ibrox for three years - and it will come down to the shareholders to decide who controls the club.
Meanwhile, former oldco director Dave King believes the current regime should invite Murray onto the board if they do remain in control.
King said: "It would really help the incumbents to get someone of Paul's experience on to the board. He's a good Rangers man and a good businessman. He knows what it's about and is interested in the club for all the right reasons. It makes good business sense
"I think it would send the right signal - almost an olive branch - to the supporters. It would be a very smart thing to do. It would be a very sensible, pragmatic and practical gesture from the board."