In April, the Pentagon authorized 4,000 National Guard troops to head to the southern border to aid USA and Customs and Border Protection.
President Trump will not be bullied into letting thousands of immigrants pour into the country.
Speaking on the condition of anonymity, an official within the Trump administration told the Post that the action was one of several measures the White House was considering as the caravan, which is reportedly still 1,000 miles away, approaches.
Thursday's move comes as thousands of Central American migrants are crossing Mexico toward the United States in a slow-moving caravan.
There are now 2,100 National Guardsmen along the border, but the DHS request could lead to the first large-scale deployment of active-duty US military forces to support the border protection mission under Trump.
Trump had tweeted Monday that he'd alerted Border Patrol and the military that the caravan was "a National Emergy", but the Pentagon said then that they'd received no new orders to provide troops for border security.
The president said nobody is getting across our border illegally and the caravan should just turnaround now, in a tweet Thursday.
Trump escalates his attack on Fed: 'My biggest threat'
But "I don't think the fact that he has publicly criticized the Fed, in any way shape or form, is going to impinge upon (its) independence", he told Reuters.
Numerous migrants are fleeing poverty and insecurity in Honduras, where powerful street gangs rule their turf with brutal violence. If the troops carry arms, it will be exclusively for self-defense. Earlier this year Mattis authorized Pentagon funding for up to 4,000 National Guard troops on the border and thus far only a little over 2,000 have been used.
"If they come here illegally with no legitimate reason to stay, they absolutely will be apprehended and removed immediately", she said, adding that the migrants should seek refuge in Mexico instead.
He told them to return to their home countries and if they want, they can apply for citizenship status like millions of others are doing.
"If someone migrates to the United States, it's to work, and working is not a crime", he said. "They will not be allowed in". It's not yet exactly clear where they will deploy.
In 2017, the US had 331,700 asylum claims, more than any country in the world, according to the U.N. Refugee Agency.
The troops are part of a security operation that is expected to be up and running by October 30. You're going to see a very secure border.