Trump mentioned New York, Chicago, Philadelphia, Detroit, Baltimore and Oakland as possible destinations for federal forces, adding that the cities' mayors are "liberal Democrats".
Trump, speaking at an event with fishermen in Maine, named White House trade adviser Peter Navarro the "lobster king" in charge of further talks.
Trump's lawyer Pat Cipollone told senators that the American people, not the Senate, should determine the president's fate.
Trump has said he was open to brokering a deal with congressional Democrats who want to protect the program in exchange for funding to build a US-Mexico border wall, a frequent campaign trail promise. He insisted during his presidential campaign Mexico would pay for the wall.
Trump is to make the announcement in a 4 p.m. EST (2000 GMT) speech.
Trump said that "workers who come to our country through the legal admissions process, including those working on farms, ranches, and in other businesses, will be allowed easy passage".
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Trump met with Kim first in Singapore last year on June 12, reaching several points of general consensus that have led to the improvement of the US-DPRK relations. However, differences between the two sides remain over key issues including the scale of denuclearization, US sanctions on the DPRK and whether to issue a war-ending declaration.
Trump has criticized Session, both in person and on his Twitter feed since Sessions recused himself from the inquiry under special counsel Robert Mueller to avoid a potential conflict of interest. Trump has said that he would have never hired Sessions if he had known he was going to recuse himself.
Trump has repeatedly described the situation at the Mexico border as a "humanitarian crisis" as speculation has increased this week that he would circumvent Congress to begin building his signature wall - a move that would be sure to draw a court challenge from Democrats who say the barrier would be barbaric and ineffective.
Trump earlier this week pushed his replacement legislation for Obamacare through the House of Representatives, and the new bill is going next to the Senate for a vote.