The Ibrox chief executive has been vociferous in his condemnation of the governing body since arriving in Scottish football and has been the subject of complaint notices from compliance officer Vincent Lunny over various comments he has made.
The Yorkshireman has gone to war with the SFA in recent weeks as Rangers continue to feel aggrieved about the treatment they received during a tumultuous summer.
Ogilvie has been forced to take a back seat for much of the saga due to his links with the Gers, where he served as secretary during the Sir David Murray reign, but hopes to sit down with Green to start building bridges between Ibrox and Hampden.
He said: "Over my years in football, it is not the first time a club has had issues with the governing body.
"I wasn't party to the discussions which took place over the last six months. I've been standing back from it, which has been awkward for me because I feel that fundamentally I've not been doing my job properly.
"One of things I would certainly like to do is sit down with Charles Green. I haven't even met the man yet. As I haven't spoken to him, I can't really quantify the depth of his feelings.
"Rangers is one of the two biggest clubs in the country and I believe that by speaking to people, issues can be resolved.
"I should be sitting down with all clubs in the game. So I'd like the opportunity to sit down with the chief executive of one of the biggest clubs.
"I've felt I haven't been doing my job in many ways over the past six months as I couldn't take part in the debate. So I would be delighted to sit down with him and open up that avenue."
Meanwhile, Scotland boss Craig Levein has admitted that he feared he would never see captain Darren Fletcher play for his country again.
The midfielder made his comeback following a chronic bowel complaint for Manchester United against Galatasaray in the Champions League last month.
"I certainly wondered if we'd ever get him back in a Scotland jersey," said Levein.
"Playing for Scotland means that much to him that he's fought his way through this illness."