The Ibrox board, headed by current chief executive Craig Mather, will meet later today, with Mr Green's position top of the agenda.
Green has angered fans with a series of controversial public outbursts following his return to Glasgow.
As revealed in yesterday's Evening Times, the three main Rangers supporters' groups said there were "significant concerns" about the behaviour of the former chief executive, now a consultant.
In a joint statement, the Rangers Supporters' Trust, Association and Assembly said: "Mr Green has clearly undermined the manager and the team.
"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."
Meanwhile, hedge fund Laxey Partners Ltd has purchased a further one million shares in the club for around £410,000.
Last week the firm, registered in The Isle of Man, bought two million shares in Rangers for £840,000. Laxey Partners has increased its stake in Rangers from 4.99% to 6.53%.
The coming days are likely to prove crucial in the battle for control at Ibrox, with Blue Knights leader Paul Murray and Scottish businessman Jim McColl calling for an EGM to be held to force through the removal of Mather, Finance Director Brian Stockbridge and board member Bryan Smart.
It is understood Laxey Partners will back the stance taken by supporters' groups, and vote in favour of removing directors.
Rangers bosses have just days to either accept the changes or hold a meeting that will see shareholders vote on the proposals.
Fans groups are also alarmed at reports that just £10million remains in the club's kitty - despite two season's worth of ticket sales and an IPO which raised £22m.
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