The move comes after the supporters' representatives held face-to-face discussions with former club director Paul Murray about his plans.
It also follows a day of revelation in the unfolding story of Craig Whyte's takeover of Rangers when the club's administrators said they had now launched their own investigation into the deal.
Joint administrator David Whitehouse said it had become apparent the proceeds from the sale of season tickets were used by Whyte to purchase his majority shareholding in Rangers.
Meanwhile, Mr Whyte issued a wide-ranging statement in response to what he called the "blizzard of questions and allegations" since the club was put into administration.
He said that every financial agreement he had made, including the season ticket deal, was in the best interests of Rangers.
He promised that, if he remained in control of Rangers when the club emerges from administration, he would consider gifting the majority of his shares to a supporters' foundation.
Mr Whyte denied he had reneged on paying PAYE and VAT since taking over, and claimed Revenue and Customs had rejected his offers of monthly payments.
And he announced he would not continue as Rangers chairman after the club was restructured, adding: "I will admit there have been times when I have wished that I had never entertained the idea of taking over Rangers."
Meanwhile, the emergence of Brian Kennedy, the multi-millionaire Scottish businessman who owns Sale Sharks rugby team, as a possible investor has also been welcomed by fans.
Rangers Supporters' Trust board member Mark Dingwall said: "The door is open to Mr Kennedy, as it is to anybody else who can facilitate the maximum input of resources."
Members of the Rangers Supporters' Assembly, Supporters' Association and Supporters' Trust met with Mr Murray in Glasgow on Monday night.
The chartered accountant, who was removed from the club board in May after Craig Whyte bought control, is interested in leading a takeover.
The Borders-based company director has formed a consortium of businessmen dubbed the Blue Knights and has spoken directly to the crisis-hit club's administrators on two occasions.
Mr Murray's plans would involve "deep fan involvement", and have been received positively by the various supporters' bodies.
Mr Dingwall added: "We met with the administrators on Saturday and we intend to approach them in the next couple of days for more talks. We want to give them time so they have something substantial to say to us.
"Paul Murray has also held a second round of talks with administrators and he is also set to report back to us with his findings and his thoughts.
"But the talks with Paul Murray were very open. Obviously, he was constrained by the fact that, as of just now, nobody knows the full financial state of the club.
"When we met, Paul was about to meet with the administrators again. He is attempting to determine the level of money that needs to be raised and applied to the club to take it forward. A lot depends on who has been assigned preferred creditor status.
"But in the meetings with Paul it emerged that the financial state of the club is such that whoever takes control needs to take the broad mass of the fans with them.
"If the deal to take the club out of administration involves the fans then we can take the club forward.
"But if somebody is interested in investing in Rangers just to make profit for themselves then they won't attract fans. The fans want to see profits returned to the club.
"We have got a lot of resources if we all work together. It can't just be a return to some of the boards that we have had in the past, groups of businessmen who decide what is the best for the rest of us."
Mr Dingwall feels the events of the past week at Rangers, when the 140-year-old institution has been plunged into administration, have underlined the need for a new approach to running the club.
He said: "It is essential that all stakeholders in Rangers need to be accommodated within a new board.
"Investment needs to be maximised.
"The old board isn't acceptable any more.
"The Blue Knights group would have a deep fans involvement.
"We have said all along that we are happy to talk to anybody who has a credible plan to rescue Rangers.
"The door is open to Mr Kennedy, as it is to anybody else who can facilitate the maximum input of resources. There should be a real thirst for fans to help. It won't work unless it is structured properly.
"We are looking to create a new type of club where the fans, the people who provide the majority of the money for the club, have a proper say in the running of the club, in its governance."
Meanwhile, Mr Dingwall gave a terse response to the statement controversial club chairman Whyte released yesterday.
He said: "My advice to Mr Whyte would be 'when you are in a hole, stop digging'.
"It would seem he has not been running the club in a proper manner in the last nine months."