Sources familiar said the discussions have been going on most of the summer.
A U.S. fighter jet shot down an Iranian drone as it approached the aircraft carrier USS Abraham Lincoln in the North Arabian Sea on Tuesday,
Trump has announced a plan for the Navy to build a new, large warship that he is calling a "battleship" as part of a larger vision to create a "Golden Fleet."
Hegseth on Tuesday cited the "fog of war" in defending the follow-up strike.
The White House acknowledges that a second strike was ordered on a boat already hit by the military in the Caribbean Sea.
Members of the U.S. military have the legal right to refuse orders they believe are unlawful, but they risk violating military laws of obedience if the order is in fact lawful, experts in military law say.