The Pentagon did not provide a comment from Feinberg and declined to make him available for an interview.
A departure by Feinberg, the billionaire co-founder of private equity firm Cerberus Capital Management, would be the most senior staff change for a department that already saw recent high-profile departures under Hegseth.
Army Secretary Dan Driscoll resigned this past week following months of tension with Hegseth, according to a source familiar with the matter. The Army declined to comment on the reasons for his departure. Navy Secretary John Phelan and several senior Army leaders also departed in recent months.
Feinberg, who vowed to accelerate U.S. munitions production, has not yet met that goal, according to analysts who say the U.S. industrial base cannot ramp up quickly. Some defense industry executives say his task was complicated by the slow pace of Congress appropriating funds despite immense pressure from the administration.
Trump increasingly expressed frustration with the lack of progress in the 6-month-old Iran war, which settled into a costly standoff between the U.S. and Iran.
One of the costs was a drawdown of U.S. weapons stockpiles. Reuters reported that the U.S. military faces significant shortages of certain munitions, which alarmed Congress and military leaders.
Trump dismissed the concerns, saying the U.S. has “far more munitions than anyone in the world.”
But in a recent exchange with Trump at Camp David, according to the Washington Post, Hegseth blamed Feinberg for letting stockpiles of long-range guided missiles and air-defense interceptors shrink.
The White House called the report “fake news.” In a statement to Reuters, chief Pentagon spokesman Sean Parnell said: “Secretary Hegseth did not mislead anyone about our munitions posture, and he did not blame Deputy Secretary Feinberg.”