The corporation reported that during a civil case last year, Mr Whyte told a court his seven-year ban from being a company director did not relate to the treatment of creditors.
But the BBC claimed the judge who imposed the ban said company assets were "put out of the reach of the creditors".
Mr Whyte has accused the BBC of being on a "witch-hunt".
His spokesman said on Monday night the allegation was "defamatory" and claimed it was "part of a concerted campaign by the BBC to embarrass Craig Whyte personally and to damage Rangers Football Club".
He said: "In specific terms, Mr Whyte totally refutes the scurrilous allegation that he may have committed perjury in a court of law in December last year. The responses he gave to questions relating to matters that took place some 17 years ago were given truthfully and to the best of his recollection."
In a statement posted on the club's official website, he said the "attack" would be "contested robustly" by Mr Whyte's lawyers.
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