The allegation was made at the Court of Session in Edinburgh, where Imran Ahmad is seeking the sum from the Ibrox club after his contract was terminated earlier this year.
The claim emerged on another day of turmoil as Mr Green's successor, Craig Mather, resigned as the Rangers chief executive.
In another twist in the battle for supremacy in the boardroom, Mr Mather left just two days after former director Paul Murray won a court battle to postpone the club's annual general meeting. It had been due to take place next week.
In Edinburgh, Mr Ahmad's legal team maintained that Mr Green told him, by letter, that his bonus would be no less than £500,000.
Mr Ahmad alleges that the letter created an obligation for the club to pay him the money.
He has raised an action against Rangers seeking the money, with the Ibrox club contesting the case.
During a preliminary hearing in the case Mr Ahmad's counsel, Ewan Campbell, argued that it would be possible to take a decision on whether Mr Green had "implied authority" as CEO in light of the company's articles of association or under the terms of a contract clause.
"These are matters which the pursuer submits can be dealt with without the hearing of evidence and can be determinative of the matter," he told Lord Woolman.
Alan Summers QC, for Rangers, said, as he understood the case, it involved an argument that is "breathtaking in its audacity".
He said the primary position for Mr Ahmad seemed not to rely on a contract clause over bonus provision, but that this was "an independent, unilateral exercise of power by a CEO" to give away £500,000.
He said both Rangers and the court needed to know where the authority to do this came from. He said they needed also to know how it could be held out to Rangers that it was somehow binding on them.
Lord Woolman said the court would require to decide whether the letter constituted a promise and, if it did not, whether it was written in terms of the bonus clause provisions.
The judge said a procedural hearing in the action would be held in December.
Meanwhile, Mr Mather's resignation follows attempts by the Rangers board to block a motion for the election of former chairman Malcolm Murray and allies Scott Murdoch and Alex Wilson as directors.
Rangers also confirmed the resignation of non-executive director Bryan Smith, leaving only Brian Stockbridge and James Easdale in post.
Mr Mather said he was leaving in the best interests of the club, which has reported losses of £14.4 million.
He added: "The facts of the matter are that the club is financially secure and in a better place than it was a year ago."