The call came after the club's prospective owner sent letters to all holders of season tickets saying cash from the sale of the passes would be placed in a secure account that would go directly to the club.
The former Sheffield United chief executive also urged supporters to renew their season tickets as soon as possible.
In the letter Green admitted there is "still uncertainty surrounding the structure of the club".
He added: "No matter the business structure going forward Rangers is and always will be Rangers... we have a very short period in which to prepare the club for next season and therefore we are asking all season ticket holders to renew as quickly as possible before the deadline on July 2.
"You can be assured that all season ticket revenues will be placed in a secure account that will go directly to the club when its structure is resolved over the coming weeks."
But Rangers Supporters Association general secretary John Macmillan said fans needed "definitive answers" before they committed themselves to the club.
He said: "There are questions that need to be put to Charles Green. We have been told it will go into a holding account but we don't know if it categorically cannot be touched by him or a consortium. We don't just need to hear that it won't be touched, we need to know it cannot be touched."
He advised fans to wait until Thursday, when the Company Voluntary Arrangement (CVA) is due to be voted on by creditors, before taking action.
One supporter, who has been a season ticket holder for 25 years, said: "We don't even know if Rangers are going to play again. I don't want to pay £420 if there's all this uncertainty."
rachel.loxton@ heraldandtimes.co.uk
