The official, speaking on condition of anonymity, did not say exactly when the troops would be deployed.
They would be joining the roughly 2200 active-duty and thousands of National Guard troops already on the border.
During his first term, Republican Trump ordered 5200 troops to help secure the border with Mexico.
Democratic former president Joe Biden deployed active-duty troops to the border as well.
Trump in his first day in office declared illegal immigration a national emergency, tasking the US military with aiding border security, issuing a broad ban on asylum and taking steps to restrict citizenship for children born on US soil.
His January 20 executive order instructed the Pentagon to send as many troops as necessary to obtain "complete operational control of the southern border of the United States".
"Within 90 days, the heads of the Defense Department and Department of Homeland Security will need to recommend whether additional actions, including invoking the Insurrection Act of 1807, might be necessary," it said.
The Insurrection Act of 1807 allows the US president to deploy the military to suppress domestic insurrection and has been used in the past to quell civil unrest.
Trump recaptured the White House after promising to intensify border security and deport record numbers of migrants.
He criticised Biden for high levels of illegal immigration although the number of migrants caught crossing illegally had already begun to fall dramatically after Biden toughened his policies last year and Mexico stepped up enforcement.
There were roughly 11 million immigrants in the US illegally or with a temporary status at the start of 2022, according to a US government estimate - a figure that some analysts now place at 13 million to 14 million.
The Coast Guard, which is tasked with maritime security and law enforcement, on Tuesday said it would "immediately surge" forces and ships to a number of areas, including the southeast border near Florida, to "deter and prevent a maritime mass migration from Haiti and/or Cuba".
It said another key area was the maritime border between Texas and Mexico in the "Gulf of America".
Trump has said he wants to change the name of the Gulf of Mexico to the Gulf of America.
