The Scottish champions called in the administrators on Tuesday after running into financial problems following a dispute with British tax authorities that could leave them facing a bill of more than 50 million pounds.
The SFA said in December that businessman Whyte, who took over the club last May and describes himself as a lifelong Rangers fan, would be investigated after Rangers confirmed he had previously been disqualified as a company director.
"The Scottish FA's previous efforts in obtaining information relevant to the 'Fit and Proper Person' requirement has been restricted by the club's solicitors' continued failure to share information in a timely or detailed manner," the SFA said on Friday in a statement on its website.
"We now feel there is no option but to undertake an independent inquiry to establish the clear facts and to determine the extent of any possible rules breaches."
Stewart Regan, SFA Chief Executive, added: "Since we have been unable to receive any detailed information requested... we feel we have no option but to appoint an independent committee to investigate a number of concerns we have raised."
The SFA have rules regarding office-bearers of member clubs and also has "the power to fine, suspend or expel any recognised football body, club, official, player, referee or other person under the jurisdiction of the Association who has brought the game into disrepute."
TRAUMATIC WEEK
Whyte described the week as "traumatic" before defending his own role at Rangers and said calling in the administrators offered the 140-year-old club a "fighting chance" of survival.
"The decision to call in the administrators was painful but it was the right thing to do," Whyte said in a statement on the club's website on Friday.
"In spite of the endless speculation and attempts at character assassination by certain sections of the media, I am 100 percent confident that the administrators' report will prove that every penny that has come in and gone out of Rangers has been properly accounted for.
"I wish to state categorically for the record now that I personally have not taken a single penny out of Rangers since I became chairman and have paid all my expenses from my own funds.
"Today I learned that my predecessor, Alastair Johnston, has urged the Crown Office to order an investigation into my takeover of the club.
"Again, I have absolutely nothing to fear because any fair investigation will prove that I have always acted in the best interests of Rangers and been involved in no criminal wrong-doing whatsoever."
VERY HARSH
Rangers, league champions a world record 54 times, were docked 10 points by the Scottish Premier League after going into administration, leaving them 14 points adrift of leaders and arch-rivals Celtic but still in second place.
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