Vincent Lunny, the SFA's compliance officer, has requested that the Ibrox chief executive justify his claims and provide proof of his allegation.
Talking before Rangers' 2-1 victory over Brechin City in the first round of the Ramsdens Cup, Green con-ducted an interview with the BBC in which he talked about the resolve to vote his club out of the Scottish Premier League and then into the bottom tier of the Scottish Football League, two separate decisions that were taken by the votes of member clubs.
"Some of it has been driven by bigotry, some of it's been driven by jealousy and some of it's been driven by all the wrong motives," Green said.
The SFA want Green to back up his claims that bigotry was involved, which would then allow the governing body to take action on the evidence he provides. They have set a deadline of August 7 for Green to respond and if he cannot justify his remarks, then Lunny can offer a fixed suspension, take no action, or pass the matter on to the judicial panel for a decision.
Before Sunday's game, Green also commented on the finances of other Scottish clubs compared to those of Rangers, despite the Ibrox side having shed millions of pounds in debt by failing to come out of administration, selling the business and assets of the club to Green's Sevco Scotland instead.
The Ibrox chief executive was also photographed applauding when the Rangers fans sang, "if you hate Stewart Regan clap your hands".
Celtic refused to comment on Green's remarks, and released only a short statement that read: "These comments are not worthy of any response from Celtic Football Club. We presume the matter would now be one for the Scottish Football Association and the Scottish Football League to deal with."