SFA chief executive Stewart Regan says alleged links between Charles Green and Craig Whyte are a “very serious issue”.
However, the governing body will wait on the outcome of a Rangers-commissioned report before deciding on any course of action.
Rangers last month appointed financial investigators from Deloitte and law firm Pinsent Masons to probe allegations made by former owner Whyte surrounding his relationship with Green during the change of ownership at Ibrox last summer.
The claims led to major shareholder Green stepping down as Rangers chief executive, although he has denied any wrongdoing.
Regan said: “We wrote to the club and expressed our concerns on a number of points related to the revelations in the press about the links between Craig Whyte and Charles Green.
“The matter was then handed over to Pinsent Masons under the stewardship of Roy Martin QC and we have agreed that we will wait until that report is concluded.
“The report is being done very much on an independent basis. The club have agreed to share the findings of that report with us so that we can get transparency on the questions that we asked.
“And until that comes out, it’s probably wrong to speculate on what might or might not happen.
“It’s clearly a very serious issue. The club is aware of how serious it is and we have been in discussions with the board of Rangers on that particular point.
“That’s why they have taken the step of appointing Roy Martin QC and Pinsents to come back with the information we seek.”
The SFA last year handed Whyte a life ban from the game after his deliberate failure to pay tax led Rangers into administration and subsequently liquidation.
However, Whyte claims he was behind the company originally designated to subsequently buy the assets and business of the club.
Green claims he and business partner Imran Ahmad, who has also left Rangers recently, only told Whyte what he wanted to hear in order to secure a deal with the club’s administrators.