Mr Green and fellow director Imran Ahmad are having a four-day, four-city tour. They in New York today after arriving in Toronto, Canada, yesterday.
They will also meet fans in Orlando tomorrow and Houston on Saturday, before flying back to Scotland for Rangers' league game against Montrose on Sunday.
Mr Green also says he plans to visit fans in Dubai and Australia in the coming months.
It is understood a number of issues will be discussed with the North American supporters, including the upcoming Initial Public Offering (IPO) where fans will have the chance to purchase shares in the club.
Mr Green said: "I am not going across the Atlantic just to talk about the IPO because there is a huge support base in North America.
"The annual convention last year came at a very bad time as far as the club was concerned.
"The administrators were here and didn't send anyone out. There wasn't a chief executive and there wasn't a board in place.
"We as a board felt there was an opportunity to get over there, even if it is a whistlestop tour.
"The important thing is for Imran and me to stand in front of these loyal fans and let them see the people in the flesh, ask questions and understand what we are trying to do, including the IPO process.
"Part of the documentation we are putting together for the IPO will also explain how we plan to expand the media side – not just in North America but for the whole world."