At a meeting with supporters last night, the chief executive confirmed he is in talks with three parties about a sponsorship deal at the club's Govan home – with shareholder Mike Ashley's SportsDirect the leading contenders.
The move to rename Ibrox is likely to split the Light Blue legions, and Mark Dingwall of the Rangers Supporters' Trust told SportTimes: "I think most fans, in their hearts, would be against it, but the financial realities mean that the club has to consider such an investment.
"We maintain that it would be far better for the club if they consider it when we return to the top flight in Scotland and also to Europe. I think that would bring major benefits to the club at that point.
"The overwhelming opinion that we have judged is that the majority of fans wish the stadium still to be called Ibrox. If it is sponsored by a company, they want to retain the title as Ibrox.
"Charles was very warmly received by the fans. He was very open and surprisingly candid. He covered a wide range of topics which was most appreciated by those in attendance."
Green's bid to find a sponsor for Ibrox is just one of his plans to increase income streams for the club after he confirmed that the Irn-Bru Third Division side would not make a profit this year, with turnover set to be below £30million.
The Yorkshireman has also pledged to stay at Ibrox for the next 11 years and will only leave if fans remove him from his position at an AGM, claiming the club will not be playing in Scotland when he does depart.
He also revealed that a new shirt sponsor and manufacturer will be announced a week on Monday, with any deals only being done on a one-year rolling contract basis.
Green has been a long-time critic of the Scottish football authorities and claimed that investors in the Middle East and Asia were put off putting money into the Gers because of the negativity towards the club in recent months.
The Ibrox chief has also vowed not to attend any meetings regarding the restructuring of our national game while Rangers did not have a vote on any proposals and claimed that some SFL clubs had given their backing to his plans for a 14-14-14 league set-up.