DHS officials said on the call that border facilities have been overwhelmed by families who can not be deported quickly because they hope to seek asylum in the U.S.
Closing the border could disrupt millions of legal crossings and billions of dollars in trade.
"Sure it's going to have a negative impact on the economy", he told reporters, while saying it was possible that only certain sections of the border could be closed.
White House Press Secretary Sarah Sanders said Tuesday the president hasn't set a timeline for action.
A senior White House official said Trump has been bombarded with a number of advisers warning against closing the border and that the current plan is not to close it during his Friday visit.
However, White House chief economist Larry Kudlow said they were working to minimize the economic impact from a closure of the border - including keeping truck lanes open.
Mexico's Foreign Minister Marcelo Ebrard is in constant communication with U.S. authorities to avoid conflict and to keep the border open, Lopez Obrador told reporters at his regular morning news conference.
USA automakers are also grappling with ebbing demand, as sales slipped 2 percent in the first quarter.
The United States gets almost 90% of its avocado imports from Mexico, and one of America's biggest suppliers, Mission Produce, has warned that the USA could run out of the trendy toast-topper in just three weeks. I mean, we have to have security.
While existing crops could be added to the food supply in the wake of a border shutdown, they would not come "anywhere close to meeting the gap in demand", Jungmeyer says.
DHS officials said border facilities had been overwhelmed by families seeking asylum, fleeing poverty and violence in Central America.
She sent a letter to Congress last week repeating numerous Trump administration's demands, including a request to quickly deport Central American minors that cross the border alone.
Officials said facilities for handling the migrants - who for the moment can not be sent back after they cross the border and request asylum - are overtaxed and understaffed, creating hazardous conditions.
"Wait times in Brownsville [Texas] were around 180 minutes, which were two times the peaks of a year ago", said a senior DHS official on a call with reporters.
Trucks inched through traffic and some stores reported fewer customers in U.S. -Mexico border towns on Wednesday, as staffing shortages tied to a surge in asylum seekers slowed checkpoints and threats of closing the border completely scared shoppers. Most foreign auto makers build vehicles containing US parts, while American vehicles use components made overseas.
Mexico is the third-largest trading partner of the United States, and is its largest supplier for agricultural products, including vegetables and avocados.
USA consumers accustomed to year-round access to fresh fruits and vegetables are reliant on Mexico's produce supply.