Reports have suggested Newcastle owner Ashley is interested in buying a stake in the Third Division Club along with two other significant investors.
And when asked whether the Sports Direct magnate will invest in the club, Green told Sky Sports News: "Hopefully, yes."
However, Green refused to reveal who the other potential investors were, adding: "Talks are ongoing at the minute so it would be premature to name them."
Ashley could be a welcome presence at Ibrox despite dividing opinion at St James' Park, although Green admitted he does not expect the businessman to plough untold amounts of money into the club should he decide to invest.
"I don't think Mike needs to throw (money into the club) and that's not the model that I think is sustainable for any football club and not Rangers," Green said.
"What Mike will do, subject to all the agreements going through, is bring the might of Sports Direct and that in itself, in my mind, will bring ?5-10million a year from merchandise in revenues back into the club.
"That is far, far more worthwhile than Mike individually signing a cheque because that's not the right way to run football clubs.
"It's about sustainability, it's about continuing revenues, it's about brand awareness and it's about developing the brand and doing it worldwide."
