President-elect Joe Biden's pick for White House press secretary, Jen Psaki, told "Fox News Sunday" that Biden will not discuss any investigation of his son Hunter with anyone he is considering to be the next U.S. attorney general.

The Delaware U.S. Attorney's Office is currently looking into Hunter Biden for possible tax fraud, and Trump is reportedly considering appointing a special counsel to ensure the probe continues after he leaves office.

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"He will not be discussing an investigation of his son with any attorney general candidates," Psaki said. "He will not be discussing it with anyone he is considering for the role and he will not be discussing it with a future attorney general. It will be up to the purview of a future attorney general in his administration to determine how to handle any investigation."

Psaki also said Biden has emphatically stated that his attorney general will "oversee an independent department," and that this person will be "somebody of the highest level of integrity."

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The discussion of the Hunter Biden probe came after Biden had told "Late Show" host Stephen Colbert that he thinks it is "kind of foul play" that an investigation into his son was "used to get to me." Psaki clarified that Biden's use of the phrase "foul play" was in reference to the politicization of the investigation, not the investigation itself.

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As for the future of Delaware U.S. Attorney David Weiss, Psaki remained non-committal, noting that this was a personnel matter and the transition team currently has more important positions to fill.

The Associated Press contributed to this report.