The New York Times said it had received some of Mr Trump's 1995 tax documents revealing $915m losses that allowed him to legally avoid paying taxes.
The real estate tycoon's camp refused to confirm or deny the report, but said the filing was "illegally obtained".
The campaign of his rival, Hillary Clinton, called it a "bombshell".
But the Republican presidential nominee's surrogates took to the airwaves on Sunday morning to defend him.
New Jersey Governor Chris Christie said the New York Times article was a "very good story" because it showcased the "genius" of Mr Trump.
Mr Christie told Fox News Sunday the report would only underline that Mr Trump is best qualified to ease tax policy on working people.