The body urged fans to hold off amid concerns about Mr Green's consortium following the former manager Walter Smith's statement yesterday that he is leading a bid to gain control of the club.
Last week, former director Dave King made a similar plea to Rangers supporters as he called for a "full and frank" discussion over moves behind the scenes related to Mr Green's bid.
The Supporters Trust statement said: "The board of the Rangers Supporters Trust welcome the bid headed by Walter Smith.
"We firmly support the view that Rangers men should be in charge at this critical time in our history and that no profit should be gained by any individuals owning the club.
"This bid is the only one which will ensure all the Rangers family are united and if it comes to fruition we can pick ourselves up and take the first tentative steps on the long road to recovery.
"We ask Charles Green to step aside from any deal to purchase Rangers and allow Walter Smith to lead us into this new era for our club.
"The Rangers Supporters Trust board calls on all supporters to hold off renewing season tickets till this situation is resolved."
New Rangers chairman Malcolm Murray, who is a fan, was earlier dismissive of groups that had previously tried to take control at Ibrox, saying that he was a "blue nose, not a blue knight".
He later said: "All of us would like to see Walter involved in some way.
"I would personally welcome the opportunity to sit down with him and explain to him the role that I am determined to fulfil in the interest of the Rangers supporters.
"It's important for everybody to be behind the club. The owners and the board want nothing but success for Rangers.
"One of the ways to ensure that is to ensure that Ibrox is full, and the sale of season tickets is an extremely important part of that."