If selected, Michele Flournoy would follow a tumultuous Pentagon period that's seen five men have the job under Trump.
The president fired Defense Secretary Mark Esper and installed three staunch loyalists to senior Pentagon policy positions.
Esper had defied the president on several occasions. His replacement, Christopher Miller, is a hawkish Special Forces veteran.
Stars and Stripes dates back to the Civil War and has published continuously since World War II, reporting on U.S. military service members around the world.
The Pentagon banned the racist flag at military institutions, with a carefully worded policy doesn’t mention the word ban or that specific flag.
When "even your own current Secretary of Defense Mark Esper breaks with you, that’s not a good week," the Fox News host said on "The View."
Military officials also ordered use of two Army National Guard helicopters to intimidate civilians in Washington, D.C., sources told The New York Times.
This is the second time this week he's made the call and broken from Trump on the need for a military response to the anti-racism protests.
The president is “a draft-dodging wannabe tinpot dictator,” said the Illinois senator and Iraq War vet. “How dare you politicize our military.”
President Donald Trump has repeatedly threatened to use the law to deploy the military to police U.S. cities.