The active-duty troops would augment the 2,000 or so National Guardsmen already deployed to support operations on the border, and could come from multiple military bases around the US.
Defense Secretary Jim Mattis was expected to sign orders at some point Thursday for the new deployment, one official said.
The troops would include doctors and engineers and would be used mainly to provide logistical support including tents, vehicles and equipment.
The official said the troops would satisfy elements of a "wish list" for military assistance sent to the Pentagon by the Department of Homeland Security, the huge US agency with responsibility for the border.
Thousands in US-bound migrant caravan pour into Mexican city
Trump earlier Thursday tweeted that "Democrat inspired" laws make it difficult to stop people at the border.
"I am bringing out the military for this National Emergency. They will be stopped!" he said.
In April, Trump said he would send thousands of National Guard troops to the southern border.
That initial authorization allowed for about 4,000 Guardsmen to be sent to the frontier, but only about half that number have been deployed.
Those troops are mainly serving in a support role to help free up border patrol officers.
Thursday's move comes as thousands of Central American migrants are crossing Mexico toward the United States in a caravan.
The issue has become a rallying cry for the US president, who has taken a hard line on illegal immigration and has repeatedly kept the story in the headlines in the run-up to America's mid-term Congressional elections that could see the Democrats regain some degree of power.
In a series of tweets last week, Trump signalled his intention to send more troops, saying that unless Mexico stopped the "onslaught" of people from Guatemala, Honduras and El Salvador, he would "call up the U.S. Military and CLOSE OUR SOUTHERN BORDER!"
He has also announced the US would start cutting aid to Guatemala, Honduras and El Salvador.
Dozens more caravan asylum seekers let in to US from Mexico
Guatemalan Foreign Minister Sandra Jovel dismissed the threat as a posture adopted for the media, however, telling reporters that the country had received no official notice of the move.
"We have had no official information, and I rather think it has all been a show for the media," the diplomat said Thursday, adding that the two countries maintained "excellent relations."
Early Thursday, the caravan set off from the town of Mapastepec in the southern Mexican state of Chiapas, moving on to the next stop in their long march north.
They were headed to the town of Pijijiapan, some on trucks but most making the seven-hour trek on foot.
Four days after crossing into Mexico, the caravan is still more than 3,000 kilometers (1,860 miles) from the US border, moving along a route that runs parallel with the Pacific coast.
"It's hard, and we know this country is dangerous too, but back in Honduras it's even more dangerous, they kill for nothing," said Josena Anibal Mejia, 27, as he walked with his daughter.
The United Nations estimates that 7,000 people have joined the caravan since it set out from San Pedro Sula, Honduras October 13.
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