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."