Following the dramatic events over the weekend, with the announcement of a binding bid by Mr Green and his 20-strong consortium, he was urged to engage with the club's fans to win over the doubters.
The bid will see the group contribute £8.5million towards a Company Voluntary Arrangement (CVA) as they attempt to save the debt-stricken club from liquidation.
General Secretary of the Rangers Supporters' Association John Macmillan has urged the Englishman to be open and honest with the Light Blue legions and distance himself from the disastrous Craig Whyte era.
Mr Macmillan said: "We will give him a cautious welcome.
"There have been reports regarding his time at clubs in the past and his business dealings, we really need to get a meeting with him for him to explain his plans and what exactly he is going to do for Rangers.
"I think one of his priorities must be to speak with the supporters' groups and answer the questions that will be raised of him.
"We need to get a clear cut idea of what his plans are.
"I know it is early days but they must have ideas of what they want to do and the fans need to know what that is, that is imperative.
"He has made statements already, so he will be tested on them.
"Hopefully we can arrange a meeting with him and he will be questioned on a lot of things by representatives of the supporters' groups."
Despite the emergence of Mr Green, the former chief executive of Sheffield United, seemingly moving Rangers a step closer to safety, plenty of work remains to be done to rescue the Ibrox club.
A CVA proposal will be sent to creditors, the largest of which are Her Majesty's Revenue and Customs and London-based firm Ticketus, within the next week as Mr Green attempts to strike a pence in the pound deal over a potential debt of more than £130m.
It is just days since American businessman Bill Miller dramatically pulled out of the race to take over the club, despite being named preferred bidder by administrators Duff and Phelps.
Mr Macmillan hopes supporters will be given the chance to play their part in shaping the Gers' future under Mr Green.
He said: "Of course, agreeing a CVA is more beneficial for the creditors, and he needs them on board to progress with that.
"It is early days, though. We had our hopes raised last week, when it looked as though something was set to happen, and we were let down.
"Things seem a bit brighter now but we need to look at it in more detail.
"I think the fans should be more involved than they have been in the past. How we achieve that, I don't know. "
Mr Green last night ruled out a fire sale of Rangers' most prized assets to raise funds and has pledged to help manager Ally McCoist in the transfer market.
Disgraced chairman Mr Whyte has seen his credibility with fans crash to an all time low in recent weeks and Mr Green has been warned actions will speak louder than words over the summer.
Mr Macmillan added: "We know that Rangers have been banned from registering new players for a year and we will have to wait until that appeal has been heard to see what we will be able to do in the transfer market.
"I don't know if there will be an awful lot of money about.
"We have to take things as they come and see what happens."