WASHINGTON—President Trump is expected to sign a directive this week that will make official his plans to revamp the U.S. asylum system, part of his broader push to crack down on undocumented migrants entering the U.S. illegally.

Mr. Trump is expected to sign the directive as early as Friday morning, before leaving on a trip to Paris, administration officials said. Last week, Mr. Trump said he intends to sign a “comprehensive” executive order on the detention of apprehended migrants, including those seeking asylum status.

According to the directive, U.S. officials will require asylum seekers to go to a point of entry along the border and make a claim for asylum, which would bar those who cross illegally. Currently, migrants who cross the border into the U.S. have up to a year to request asylum, regardless of how they got here.

The argument being made by the administration is that this change will enable safer, more orderly processing and better resource planning, an official said.

The officials, who have seen a draft of the directive, said the intention is to implement the directive temporarily, although a time period wasn’t specified.

Mr. Trump said last week he wants to keep undocumented immigrants apprehended at the border in detention until their legal cases are heard, rather than allow them to be released into the U.S. to await a hearing.

The new directive follows Mr. Trump’s order to send thousands of U.S. troops to support border-control efforts. The president has also said he would sign an executive order ending birthright citizenship for children born in the U.S. to illegal immigrants, a proposal legal scholars say would be unconstitutional.

Earlier this year, officials at the Department of Homeland Security publicly encouraged would-be asylum seekers to ask for refuge at points of entry, saying that was the only legal way to apply for asylum at the border. Since spring, foreigners have routinely had to wait days or weeks to cross the border at entry points to seek asylum.

Mr. Trump ramped up his immigration message in the days leading up to Tuesday’s midterm elections, describing a caravan of destitute Central American migrants heading northward toward the U.S. border as an “invasion.”

With Democrats winning control of the House of Representatives on Tuesday, immigration is now poised to be one the biggest battles for the president. Democrats are likely to push back on his hard-line immigration policies and his plans for a border wall with Mexico.

“We need the wall,” Mr. Trump said Wednesday during a White House news conference. “Many Democrats know we need the wall. And we’re just going to have to see what happens. I mean, I will be fighting for it.”

Write to Vivian Salama at vivian.salama@wsj.com