More than 300 supporters attended a fans' forum at the Govan club on Friday night which was addressed by Green and Newcastle United managing director Derek Llambias.
Newcastle owner Mike Ashley has held talks with Rangers over purchasing the naming rights. Ashley is a Rangers shareholder and his SportsDirect firm are the "official retail partner" of the Glasgow club.
A statement on Rangers' website said: "Following a discussion on the potential commercial opportunities for the club through naming rights, fans gave the go-ahead for Green to progress the issue but made clear that any renaming of the stadium should include 'Ibrox'."
Green said: "I am very pleased and heartened by the supporters' approach to this and we will take things forward as soon as possible."
Manager Ally McCoist said the retention of the word "Ibrox" would be the least he would hope for. He added: "I am reasonably open-minded about the whole thing. There is a big part of the traditionalist in me, which would say leave it alone, but I understand there's an opportunity to raise income.
"I think the most important thing is that the fans' views are taken on board because it really is such a controversial topic. No matter what happens, people will not be happy. All I would hope for is that the majority are happier."
McCoist, who has tied up Kal Naismith on a new two-year deal, also spoke out about league reconstruction yesterday, describing it as "madness" that clubs do not yet know if it will be in place for next season. The proposed 12-12-18 set-up would leave Rangers playing in Scottish football's bottom tier for a second season, even if they win the Irn-Bru Third Division this term. McCoist said: "We should have been told a long, long time ago what's happening next season."
Hindered in his rebuilding attempts due to a transfer embargo, McCoist says the uncertainty over the league structure has added a further barrier.
"How can I attempt to sign any player when he does not know what league he will be playing in?" he added. "It's madness. It will affect sponsors, who will say, 'what league are you in?' and you say 'we'll get back to you on that one'.
"It's not fair on our punters either. Why should our fans be asked to put their hands in their pockets for us to play in a league that we do not know we will be in yet?"