The Ibrox board are due to meet on Monday to discuss the future of the Yorkshireman and his involvement with Rangers after he made a controversial return earlier this month.
Green resigned as chief executive in April amid allegations of links to former Rangers owner Craig Whyte and anger over racist comments made about former club director Imran Ahmad - a statement for which he was fined by the Scottish Football Association.
An independent investigation said that Whyte, the man who set Rangers on the path to liquidation when he put them into administration 18 months ago, had not invested in the current Rangers set-up.
But Green has faced fresh anger after telling boss Ally McCoist he would have a "problem" if he failed to lead the team to a domestic cup win while also backing a £3.4million legal bid launched by Ahmad against the Glasgow side after he too was forced out of the club.
Meanwhile, Rangers are considering an official request from a group of shareholders to hold a extraordinary general meeting to vote on their proposal to remove new chief executive Craig Mather, Brian Stockbridge and Bryan Smart as directors and replace them with Paul Murray and Frank Blin.
Now in a joint statement issued by The Rangers Supporters Assembly, The Rangers Supporters Association, and The Rangers Supporters Trust, the board has been told the club's fans want Green out.
The statement read: "There are significant concerns among our worldwide fan base over the conduct of former CEO, Charles Green.
"Mr Green has been very outspoken in the media, and has clearly undermined the manager and the team. He is also purported to be giving support to a financial claim to be made against the club which we feel represents a conflict of interest for him and the club.
"We strongly urge the board to terminate Mr Green's consultancy role and make a clear decision to either accept the requisition to make changes to the board, or confirm the date of the EGM."
The three supporters' groups have also expressed anger that around £22million raised by an initial public offering of shares has been frittered away, with just £10million from season-ticket sales and sponsorship deals left in Rangers' accounts.
Billionaire businessman Jim McColl is involved in the call for an EGM and wants to install Blin to carry out a forensic examination of the club's finances amid concern over corporate governance.
The supporters' statement added: "We were greatly concerned at the fans' meeting on August 8 to learn that there is only £10million in the club's account. This is especially worrying considering the club has benefited from two seasons worth of season ticket sales (over 70,000) as well as the £22million raised in last year's IPO.
"From the wording of the EGM requisition, and the media comments of Jim McColl, we understand the requisition does not mean a potential takeover of the club but is an attempt by a large group of shareholders to have their views represented on the board and to bring much-needed stability to the club.
"We are confident that fans will support Mr McColl and his colleagues and we can also work with them towards a fan ownership/representation model."
Meanwhile, Rangers confirmed to the Stock Exchange that Laxey Partners last week bought another million shares in the club.
It comes just a week after the company purchased a tranche of two million shares. The Isle of Man-based investment firm - which had previously agreed to buy Green's shares once he is permitted to sell them in December - a year after the club was floated on the stock exchange - now holds a 6.53 per cent stake in the club.
- Sports & Recreation
- Rangers Supporters Trust
- Craig Whyte