Green has apologised for a remark about fellow director Imran Ahmad that has led to a Scottish FA investigation.
Former owner Craig Whyte has also alleged close links with the pair during their consortium's purchase of the Ibrox club's assets last year.
According to BBC Scotland, Green and Ahmad are compiling a dossier, which could be handed to the police as early as next week, with a view to making an allegation of blackmail against Whyte and his business partner, Aiden Earley
That coincided with Rangers Supporters' Trust issuing a statement urging Green and Ahmad to take legal action against Whyte.
It has also asked the board to clarify Green's position as chief executive in light of the recent controversy.
On the charge of racism against Ahmad, one of the largest institutional shareholders in the Ibrox club told BBC Scotland it was "confident that the board and their advisers are looking into these matters and we're looking forward to hearing their views".
Despite Green apologising for any offence caused by his remark about Mr Ahmad, the SFA citing the chief executive for comments "of an offensive and racist nature".
Now the chief executive faces being questioned by his boardroom colleagues not only about the SFA's allegation of bringing the game into disrepute but over the claims about his links with Whyte.
Rangers went into administration during Whyte's tenure and police this week carried out a series of raids relating to the Scottish businessman's purchase of the club from Sir David Murray.
However, Whyte last week gave BBC Scotland documents, text messages and secret recordings to back his claim that he still owns Rangers' assets and that Green had agreed to be his front man.
Whyte claims he still owns the assets of Rangers despite the takeover by Green
Green responded by revealing that Whyte had deposited £137,000 in a Rangers account and would not take the money back.
The chief executive insisted he had no financial tie-in with Whyte, but the claims led the SFA to write to Green asking for clarification about his dealings with the former owner.
The governing body ruled last year that Whyte is unfit to be involved in the running of a football club.
In a statement, the supporters' trust said the board had "the competency and authority to deal with the matters surrounding Mr Green's recent performance".
"Our club needs clarity over two major issues: the future of Charles Green and the ongoing claims of Craig Whyte," it added.
"The proper places for these two to be handled are, respectively, the Ibrox boardroom and a court of law.
"With regard to Mr Whyte's claims, the board can question the directors and employees concerned in a confidential manner.
"His allegations appear so outrageous and injurious to the club that only a court appearance will force him to provide conclusive evidence of his claims.
"As he is alleging collusion between himself, Mr Green and Mr Ahmad, we believe that the situation now requires judicial examination and recommend that Mr Green and Mr Ahmad instigate legal proceedings against Craig Whyte without delay."
Whyte described the accusation of blackmail by Green and Ahmad as "comic".
"Mr Green has publicly admitted defrauding me on the Sevco deal," he said. "I am seeking to put that right by taking legal action.
"This must be the first alleged blackmail in history where the person making the allegation has actually received money rather than the accused.
"Following through their bizarre logic, anyone who takes legal action against them is a blackmailer."