Reports have claimed that two other billionaires are interested in buying a stake in the Ibrox outfit, who will be forced to work their way back into the Scottish Premier League from the bottom tier.
Green has insisted that he does not expect Ashley to "throw money" at the club and instead hopes the Buckinghamshire-born businessman can be part of a sustainable plan going forward.
When asked if Ashley could be involved, Green told Sky Sports: "Hopefully, yes.
"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.
"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 £5-10 million 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."
Despite the club's position in the fourth tier, Green hopes to build up the club's reputation worldwide in order to return it to the top of Scottish football in a good financial state.
"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," he added.