The investment professional, who asked not to be named, is a long-standing season ticket holder at Ibrox, said he has consulted a "mainstream" law firm in London to investigate the options available.
He intends to take the matter further down the legal route if the board at Rangers International Football Club (RIFC) are unable to provide answers.
He said he wanted to know what exact efforts the current board (RIFC) has made to uncover who is behind Margarita and Blue Pitch.
He said: "I am getting a bit irritated with this obscurity about Blue Pitch and Margarita.
"If [the board] say we don't know then I want them to make a public report saying that. If they do know who is behind it they should be telling us.
"I think the fans really need to know the identities of the people behind these holdings. That is only fair."
Blue Pitch has four million shares in RIFC, equivalent to more than 6% of the share capital, with Margarita holding 2.6 million, or 3.6%.
Both are believed to be backing the current regime at the RIFC annual general meeting on December 19.
Shareholders are being asked to vote at the AGM whether to retain chairman David Somers, chief executive Graham Wallace, finance director Brian Stockbridge and non-executive director Norman Crighton.
Along with several other resolutions there will also be votes on whether to accept Malcolm Murray, Paul Murray, Alex Wilson and Scott Murdoch.
The fund manager indicated he will pursue the identities of Blue Pitch and Margarita regardless of how the AGM turns out.
He said he would like to have access to the latest financial incomings and outgoings at RIFC and see details of commercial contracts.
The possibility of disenfranchising secretive shareholders was raised last month by former RIFC chairman Malcolm Murray.
That option is thought to relate to a section of the Companies Act 2006 which states a company has the right to know the beneficial owners of shares held in nominee accounts.
A company has to maintain a register of such interests which must be available for shareholders to see.
If that is not made available one possibility is for the voting rights of the shares to be suspended.
A spokesman for Rangers said: "I find it quite ironic that an anonymous shareholder is requesting this information. It is irony piled on irony.
"There is nothing sinister about the Blue Pitch Holdings and Margarita Funds, Malcolm Murray knows who they are.
"This is a pathetic, last-minute bid to influence the AGM and it is futile and it will fail."