Former Trump adviser was sentenced in January to four months for contempt of Congress after refusing to comply with a subpoena from the House Jan. 6 Committee.
Navarro and the Justice Department clashed over his claim that President Trump invoked executive privilege.
A jury recently awarded Ms. Freeman and Ms. Moss nearly $150 million.
Rudy Giuliani is facing tens of millions of dollars in damages.
Trump’s cases in New York and Washington have prompted a fierce debate over how far judges can go in limiting free speech.
Special Counsel Jack Smith’s team argues the gag order doesn’t violate the Constitution.