Gers chief executive Green launched a share issue last week he hopes will raise £20million for the Ibrox club. But the English businessman has publicly admitted in the past his group are looking to make a profit on their £5.5million investment.
And doubts remain among large sections of the Light Blues support about where their money will go if they choose to invest.
However, Green has met with official supporters' groups and confirmed any cash raised will all be ploughed into Rangers.
"In recent meetings, both with ourselves and other fans' organisations, many of the issues that have been troubling fans have been addressed," said Rangers Supporters Trust spokesman Mark Dingwall.
"The money from the share issue will remain in the club and won't be distributed to his group through dividends.
"In addition, the property assets of the club will remain within the club and will not be sold off. We welcome Mr Green's openness in dealing with the fans."
Dingwall added: "We have asked Mr Green how his group plans to make money and he told us by uplifting the share value.
"The only way they can do that and crystalise their investment is by having a properly run club. It is in their best interests for the club to flourish."
He went on: "After all that happened under the stewardship of the David Murray and Craig Whyte regimes, Mr Green's group was always going to be examined very carefully.
"But so far I think many fans have been very positive about the initiatives put forward by Mr Green and his group.
"There has also been mention of non-executive directors being appointed to oversee the corporate governance of the club.
"Having a unified fans' voice and representation on the board is positive. Fans are capable of playing their part in the running of the club."