Without proof, Trump's top trade adviser pushed that now-departed NSC official was Anonymous

Once the unsubstantiated rumor began circulating inside the West Wing, the book's publishers denied Coates was the author, but their denial did little to stop Navarro from continuing to insist it was her, two people said.

For the last several weeks, Navarro has been on a hunt to determine who is Anonymous, two people said, a move that would likely ingratiate him with the President.

This was first reported by the Daily Beast.

Several officials were initially amused by Navarro's tactics, but then became concerned that it could affect Coates' standing with the President, the same officials said.

Several officials who heard Navarro push this said they do not believe Coates is the author and several described her as loyal to the President's agenda. However, the workplace became untenable given these dynamics, so Coates began looking for an exit, officials said, which led to her move to the Energy Department on Thursday.

Both Navarro and Coates declined to comment when reached by CNN.

Asked Tuesday if there was a search for who "Anonymous" was, Trump said: "Yeah there is, it's not so much a search, I know who it is. I can tell you that but I know who it is."

The national security adviser, Robert O'Brien, elevated Coates to deputy national security adviser when he took the job last fall.

A week ago he insisted she would not be moved out of the National Security Council, but within days it became apparent that was not a long-term option. He confirmed her move to the Department of Energy on Thursday.