The 48-year-old journalist made the demand on Wednesday's episode of Tucker Carlson Tonight.
During her first televised interview since her departure from Today, Kelly spoke about the allegations published in Ronan Farrow's new book Catch and Kill. In addition to detailing the sexual misconduct claims made against Lauer, Farrow accused NBC News of trying to shut down his reporting of the Harvey Weinstein scandal.
"The question is what did they know about Matt Lauer prior to the time the woman came forward, who was ultimately his downfall?" she said. "She came forward—her name is Brooke Nevils—made an allegation against Matt Lauer and the company's whole defense to Ronan's book essentially has been, 'That's the first we ever knew about Matt Lauer. There was no deal between us and Harvey Weinstein to cover up for Harvey Weinstein so that he wouldn't report on Matt Lauer because we didn't even know that Matt Lauer was doing this. We had no notice of it whatsoever.'"