Concern is growing that mystery is continuing to surround the identities of those behind Blue Pitch Holdings and Margarita Holdings.
Both funds were involved in Mr Green's initial purchase of the oldco, liquidated Rangers' assets in the summer of last year.
The two shareholders have currently handed their proxy votes to Sandy Easdale who, with brother James, owns or controls about 25% of the stock in Rangers International Football Club.
An annual general meeting (AGM) is looming and consensus needs to be found between shareholders to make new boardroom appointments as Rangers have been left with only two members.
The fans have also demanded that the board arrange the AGM as quickly as possible and for the Easdales to reveal their plans for the club and their motivation for being involved at Ibrox.
A joint statement from the Rangers Supporters Trust, the Rangers Supporters Association and the Rangers Supporters Assembly said: "Given the level of concern among fans regarding the ownership and finances of the club over the recent past, we feel it is vitally important that the individuals behind Blue Pitch Holdings and Margarita Holdings are made known to remove any doubt that there are connections to either Craig Whyte, Imran Ahmed or Charles Green.
"Walter Smith and Ally McCoist have spoken of the need to 'cleanse' the club of all the rumour, speculation and innuendo. The identity of the individuals behind these two shareholder groups is a significant part of that process."