On Tuesday, Kudlow slammed Navarro for his remarks on the White House's ongoing trade negotiations with China. Washington and Beijing have struggled to reach a new trade deal and de-escalate tensions that have led to mounting tariffs.

Despite the tensions, neither official is expected to leave the administration soon, said the source, who declined to be named. President Donald Trump could also change his mind at any time about Navarro's role.

The White House has deliberately curtailed trade advisor Peter Navarro's public profile amid a clash with top economic advisor Larry Kudlow, a person with knowledge of the matter told CNBC on condition of anonymity.

Last week, Navarro said a potential deal with China "will be on President Donald J. Trump's terms. Not Wall Street's terms." Navarro, who has taken an aggressive stance toward changes in the U.S. trade relationship with China, contended that "there will be a stench around any deal that's consummated" because of Wall Street's involvement. The comments helped to sink the stock market.

Kudlow told CNBC on Tuesday that Navarro "was not speaking for the president, nor was he speaking for the administration."

"His remarks were way off base. They were not authorized by anybody. I actually think he did the president a great disservice," said Kudlow, the director of the National Economic Council.

Trump plans to meet with Chinese President Xi Jinping at the G-20 summit in Argentina this month. The leaders are expected to discuss trade.

Trump has pushed for Beijing to make changes to address alleged Chinese theft of American intellectual property and reduce the U.S. trade deficit with China. He has threatened to put tariffs on another $257 billion in Chinese imports, on top of the duties already in place on $250 billion in goods.

Navarro has reportedly been marginalized in the White House before. According to Bob Woodward's book "Fear," officials such as chief of staff John Kelly would work to limit Navarro's access to the president.

Navarro is considered the advisor who most fuels Trump's fixation on reducing trade deficits. Trump has repeatedly described trade deficits — which mean one country imports more goods and services from a trading partner than it exports to that nation — as "losing" money. It is not clear that the U.S. trade deficit with China has harmed the American economy.