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 the Light Blues over purchasing the naming rights.
Ashley is a Rangers shareholder and his Sports Direct firm is the official retail partner of the Glasgow giants.
A statement on the club's website read: "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 in the title."
Green said: "I am very pleased and heartened by the supporters approach to this issue and we will take things forward as soon as possible."
Meanwhile, youngster Kal Naismith has signed a new two-year deal with Rangers.
Naismith told the club's website: "It's brilliant to be staying on at the club and staying for two years is great as the gaffer is showing a bit of faith in me.
"Hopefully in that time I can get a chance in the team, take it and kick on, becoming a first-team member. I feel that I know what I want now and I know what I need to achieve to make it as a footballer. I'm ready to try to do that.
"I'm trying to be more professional about things so I'm training hard and trying to get in the team."