The call came after Mr Green sent letters to all ticket holders 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 tickets as soon as possible.
In the letter Mr 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 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 John Macmillan, general secretary of the Rangers Supporters' Association, 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 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 is due to be voted on by creditors, before taking action.
One supporter, 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 is all this uncertainty."