Murray, who sold Rangers to Craig Whyte 13 months before the club was consigned to liquidation, was the instigator of the controversial tax scheme that remains the subject of both a tribunal and Scottish Premier League inquiry.
Green revealed Murray had agreed to help him deal with the fallout from the use of the Employee Benefit Trusts.
Green told Rangers TV: "Sir David is really keen to help the club. I welcome that and I appreciate the time we spent together.
"He has some clear views in terms of EBTs. No-one knows better than Sir David about that and he is prepared to do whatever is required to set the record straight."
Green also revealed the club could acquire Edmiston House, a three-storey building behind the Copland Road stand, from Murray, who used it to base one of his companies.
The building, which once housed the ticket office and a social club, was bought in 2002 for more than £1.1 million.
"From a tangible point of view one of the things we went to discuss was trying to acquire Edmiston House because that would be very important to my plans," Green said.
"I think we have agreed in principle a deal on that. So he has helped the club by coming to an acceptable deal on that and that is very much appreciated."