Politico reported Tuesday that Newman once served as Gregg's congressional chief of staff.
Gregg was tapped to be U.S. commerce secretary by President Barack Obama. Judd has said he would only take the post if he was replaced by a fellow Republican.
Andrew Lietz, the former chief executive of electronics manufacturer Hadco and a former New Hampshire university system trustee, told the Manchester (N.H.) Union-Leader that Newman would be "a terrific choice."
He called her "a person of great integrity and a very good listener. She knows how to work well with people of differing viewpoints and is very thoughtful as she arrives at decisions," the newspaper reported.