The former chairman, who sold Rangers to Craig Whyte for a nominal sum 13 months before the club PLC was consigned to liquidation, was the instigator of the Employee Benefit Trust (EBT) tax scheme that remains the subject of both a tax tribunal and a Scottish Premier League inquiry.
However, the Rangers chief executive said fans should move on from their concerns about Sir David, saying the former chairman was not the first person to have "made a mistake" with Craig Whyte.
Sir David previously said he made a huge mistake by selling, claiming he was "duped" into believing Whyte had the cash, the clout and the passion to run Rangers. He said he would not have sold the club to Whyte if he had known the risk of the crisis that would follow.
However, the Rangers Supporters' Assembly warned a sizeable minority of fans will not welcome Murray's involvement.
Mr Green, who bought the assets and business of club owners Rangers Football Club plc and re-launched as a new company, revealed Sir David had agreed to help him deal with any fallout from the EBT issue.
He also revealed the club could acquire Edmiston House, a three-storey building behind the Copland Road stand at Ibrox Stadium, from Sir David. The steel tycoon used it to house Response, a call centre business with two other sites in Glasgow which together employs around 1800 people.
Mr Green said: "We had a good chat around a number of subjects and Sir David is really keen to help the club. I welcome that and I appreciated the time we spent together.
"Yes, he did sell the club to Craig Whyte and that is history now. Sir David wouldn't have been the first person who made a mistake with Mr Whyte.
"But we all have to move on. In my mind he has been helpful to me and while there may be some fans who are unhappy with Sir David, there were lots of fans unhappy with Charles Green, and I'd like to think we moved forward from that as well.
"He has some very clear views in terms of EBT and there is no-one knows better than Sir David about that. He is prepared to do whatever is required to set the record straight.
"We covered a number of issues and I am looking forward to seeing him and meeting him again because he has a wealth of knowledge of Rangers football club. He was very important to this club over the last 20 years."
Andy Kerr, president of the Rangers Supporters' Assembly, said there would be "an element of nervousness" about Murray's involvment. "Forgive Sir David? There's a fair body of people that would say no," he said.
"There is a proportion of people who say Sir David Murray is the root cause of the problem and we don't want him to darken our door again. Murray has been at the centre of everything up to the point where it all went wrong, so he is obviously a key source of valuable information.
"If that is helpful for us, then fine. I am pretty sure the way Charles Green has been operating that he wouldn't go down that route unless he felt there was some benefit to take the club forward."
Mr Green would not divulge what use he would use Edmiston House for except to say "that would be very important to my plans".