Mr Trump also denied reports that he was seeking a high security clearance for any of his children - though he did not mention his son-in-law, Jared Kushner.
But this morning, ABC reported that a staffer had asked for security clearances for Trump's children; their source was an aide on the Trump transition.
Stories about Trump's transition dominated the front pages of both the Washington Post and the New York Times on Wednesday, as several well-known Republicans have been pushed aside in recent days.
One of those pushed out was ex-Rep. Mike Rogers of Michigan, the former chairman of the House Intelligence Committee.
Reports indicated that Rogers got the boot in part over a report issued by his committee several years ago, which - like other Republican investigations in Congress - found no support for the charge that there was a "stand down" order during the Benghazi attacks.
Rogers had been brought in by Gov. Chris Christie of New Jersey, but when Christie was pushed out in recent days, Rogers was sent packing as well, according to numerous reports.
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