The new measures under preparation would continue to allow foreigners to request asylum if they enter the country legally at US ports of entry, but not those who cross without authorization, administration officials said.
The American Civil Liberties Union, a group that defends individual rights, declared the move "illegal".
Currently, U.S. asylum rules do not bar people who enter the country without authorization, and the Immigration and Nationality Act, which governs the U.S. immigration system, specifically allows people who arrive in the United States, whether or not they do so at a designated port of entry, to apply for asylum.
They said staff already had other duties processing legal travellers, inspecting cargoes and policing for drugs.
Trump is using the same powers he used to push through a version of the travel ban that was upheld by the Supreme Court. They are now about 600 miles away. The proclamation puts into place regulations adopted Thursday that circumvent laws stating that anyone is eligible for asylum no matter how he or she enters the country.
Many politicians on both sides of the aisle agree that the United States immigration system is hugely inefficient and unable to cope with demand.
The US president railed against the caravan in the lead up to the election, telling the refugees and migrants they would not be welcomed in the United States. About 4,800 migrants are sheltered in a sports complex in Mexico City, some 600 miles (965 kilometers) from the USA border.
But directing the migrants to the official ports could create massive backups among applicants on the Mexican side of the border.
Members of one of the migrant caravans riding on a truck in Donaji, Mexico, last week.
A senior administration official said Thursday that the vast majority of such claims are "non-meritorious".
Less than 10 per cent of cases result in asylum being granted, the government says.
Detention capacity at USA immigration jails already almost maxxed out, and court-imposed limits on the government's ability to hold children in immigration jails for longer than 20 days mean most migrant families who arrive seeking protection are still likely to be released pending a hearing.
That way, he said, courts will "handle those claims in an expeditious and efficient manner, so that those who do actually require an asylum protection get those protections". It's unknown whether those in the caravan, many fleeing violence in their homeland, plan to cross illegally.