Sir Gus said the Forfeiture Committee would "look at" the situation in relation to the ex-chief executive, although it will stop short of a formal investigation.
In a letter to Labour backbencher Gordon Prentice, he stressed that the committee usually only responded to "judgments by the Courts or by the appropriate regulatory or other professional bodies".
"I will, of course, put the points you have made to the Forfeiture Committee, which will look at them against the background I have sketched out above and decide whether any action on its part is appropriate," he went on.
Dozens of Labour MPs have called for Sir Fred to lose his title, amid anger over his handling of the stricken banking giant and his £700,000-a-year pension.
Mr Prentice said: "Sir Gus tells me forfeiture normally follows a finding of guilt by a regulatory, judicial or other competent authority on the basis of evidence put to it.
"Sir Fred was the central figure in the collapse of a major Scottish institution.
"In these circumstances, retaining a knighthood awarded 'for services to banking' strikes me as bizarre."
Sir Gus wrote that the Forfeiture Committee "does not have a role in supervising or monitoring the subsequent activities of all those who have been granted honours by the State".
"Its role is rather to consider cases for forfeiture in the light of evidence put to it and relevant precedents. The normal sources of such evidence are judgments by the courts or by the appropriate regulatory or other professional bodies," he said.
He said in previous forfeiture cases there had been a "clear determination of guilt by the appropriate regulatory, judicial or other competent authority on the basis of evidence put to it".
"The Forfeiture Committee then decided whether the individual's honour should be forfeited. The Committee is not normally involved prior to any findings by the appropriate authorities."