Smith had been part of a consortium that launched an unsuccessful bid to buy the stricken Glasgow giants from administrators Duff and Phelps last June.
But Gers chief executive Green is still keen for the hugely experienced coach to serve on a new club board that will soon be set up to focus solely on football matters.
He said: "Walter Smith knows the club better than anyone. I'd like to get him on the board or as an advisor.
"Rangers need people who understand football, Rangers people who understand the culture. We're short of that.
"Nobody round the board understands football. My knowledge you could carry in a mouse's handkerchief. There are a number of people who know more about Rangers than I will ever know. I want to draw on all of these people."
Green added: "We've said we will have a plc board, which is a stock exchange requirement, and we will have a football board.
"We will welcome a fan representative on that board, and it will be the heartbeat of Rangers.
"It should carry a number of people, six, seven, eight, who talk about youth development, the team, fans, all the interests of what make Rangers great.
"We want it to be inclusive, not exclusive. Fans have seen and heard what we plan to do, we've done everything we said we were going to do."
Meanwhile, Green has stated he had no problem with manager Ally McCoist deciding to back Smith's bid to take over the club in the summer.
He revealed: "Ally came in when Walter had launched his bid and said, 'I'm in a real difficult situation. Walter is my best pal, a friend for 20 years, I can't support you'.
"I said, 'Great, never turn your back on Walter, I don't want you if you can be disloyal to him'."
Meanwhile, Green declared the share issue is being launched now so fans have the opportunity to buy into the club when the share price is low – and stressed the money was not needed to cover running costs.
He said: "If I float it next year, the club will be worth more and fans would have to pay more. It was stated publicly in the first document we put out to raise funds.
"In terms of monthly requirements, we can't run out of money. The player wage bill was £27million, now it is less than £7m."
Green has reiterated his belief that Rangers will leave Scotland and play in a new European league in the future.
He stated: "There will be a European league, I'm convinced of it. Not next week, but in five to 10 years.
"Manchester United listed and floated in New York with a value of £1.2billion. Everton are up for sale at £300million, £400m.
"How can they be valued at those numbers and Rangers only be valued at £30m? It is inconceivable that those values will stay."