The Union of Fans - a coalition group representing six supporter bodies - have released a statement through Press Association Sport demanding answers about what happened to the Yorkshire businessman's 7.68 per cent stake in the club after he called a halt to his second stint with the club as a paid consultant last August.
It comes after former director Dave King spoke out on Saturday about his fears that it was "quite possible that Charles Green is still de facto controlling the club".
King now plans to travel to from his base in South Africa to Scotland to step up his bid for boardroom change after his attempts to invest in the club in order to avert a planned downsizing of the club's budget were thwarted by the current Ibrox regime.
Green stepped down as the Light Blues chief executive last April after it was alleged he had links to former owner Craig Whyte, although he was later cleared by an independent commission.
The 60-year-old then returned to the club during the summer but had his consultancy contract terminated after a fall-out with boss Ally McCoist.
It was announced then that Green would sell his stake in the club to investors Sandy Easdale and Laxey Partners but the fans say they have no record of the Easdale trade ever tacking place and want an explanation.
The Union of Fans' statement said: "We welcome the fact that Dave King has committed to travelling to the UK. We very much look forward to meeting him in the near future to push things forward.
"We also note that, like us, he shares a fear that Charles Green and the people he represents are still de facto in control of our club.
"We would like this board to explain just what has happened to the 5 million shares Charles Green awarded himself at 1 penny each and which constituted a 7.68 per cent stake in Rangers.
"We are aware that some of those shares are now in the hands of Laxey. It was also widely publicised that Green had proxied his shares to the Easdales and struck an agreement to sell those shares to the Easdales in December 2013. But no record of such a share trade exists.
"Also the Easdales do not appear to have increased their notifiable interest in the company according to the most up-to-date information available.
"It is entirely unclear who now holds the balance of Mr Green's shares and if indeed they have even moved out of his control."
Demanding the right to examine the club's register of shareholders, the fans group added: "Dave King is quite correct to express his fear that Charles Green and those he represents are possibly still controlling Rangers.
"Just as we, as supporters and shareholders, are right to exercise our legal right to view the up-to-date shareholders register. Once again, we simply ask this board to answer the perfectly reasonable questions they are being asked and to not just speak about transparency but actually provide it."
Graham Wallace, the current Rangers chief executive, appealed for the supporters' trust this week after they responded angrily to news the club had been forced to take out a £1.5million from Easdale and Laxey Partners just to see the League One champions-elect through to the end of the season.
Laxey stand to make a £150,000 profit or land the equivalent in shares from their part of the deal but the Union of Fans say those terms are wildly generous.
And with Wallace little more than halfway through the 120-day review of the club's operations announced at its AGM back in December, the fans are already raising questions about his leadership.
Their statement added: "We also note that Graham Wallace recently attempted to justify the £1.5m loan from Laxey and Sandy Easdale, by indicating that it was part of a business plan he 'inherited'.
"Just who did he inherit the business plan he is implementing from? Charles Green? Brian Stockbridge? Imran Ahmad?
"Also, why is he still implementing a business plan which is so clearly flawed? Particularly when it is clear that alternative routes are and have been available."
Rangers have rejected internet rumours that the club will enter administration for a second time on Wednesday.
A spokesman for the club said on Sunday: "There is absolutely no truth in these claims which appear to come from agenda-driven bloggers who are out to damage the club.
"There is no chance of administration while there is no board meeting tomorrow. This is all completely false."
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