In a speech to be delivered from the White House, Trump will continue to demand $5.7 billion in wall funding, but also offer backing for legislation to protect young undocumented immigrants known as “Dreamers," as well as temporary protected status (TPS) holders, the source said, confirming a report by Axios.
Vice President Mike Pence, White House chief of staff Mick Mulvaney and Jared Kushner, the president's son-in-law and a senior White House adviser, have been instrumental in crafting the deal, the source said.
Trump is to make the announcement in a 4 p.m. EST (2100 GMT) speech.
The source said Trump does not plan to declare a national emergency along the U.S.-Mexico border, a step he threatened to take earlier in his struggle with Congress over the shutdown triggered by his wall-funding ultimatum.
Declaration of an emergency would allow Trump to bypass Congress to pay for a border wall, although such a step would likely prompt a legal challenge over constitutional powers from congressional Democrats.
Trump is under pressure to end the shutdown with Americans increasingly blaming him for refusing to sign spending bills that would provide paychecks for 800,000 federal workers who have been idled or working without pay for nearly a month, the longest government shutdown in US history.
Trump told reporters on the White House South Lawn on Saturday he has no personal feud with House of Representatives Speaker Nancy Pelosi, the top US Democrat. She and other Democrats oppose the wall, calling it too expensive, ineffective and immoral.
"Whether it’s personal or not, it’s not personal for me," Trump said. "She’s under total control of the radical left. I think that’s a very bad thing for her. I think it’s a very bad thing for the Democrats."
Trump also said he was concerned about a new wave of immigrants moving north through Mexico toward the US border.
"I’m disappointed that Mexico is not stopping them. I mean, Mexico seems unfortunately powerless to stop them," he said. "If we had a wall, we wouldn't have a problem."
The "Dreamers," who are mostly Latin American, are protected from deportation under the Deferred Action for Childhood Arrivals (DACA) program. The program protects certain people who illegally entered the country as children, providing about 700,000 immigrants with work permits, but no path to citizenship.
Former Democratic President Barack Obama put DACA in place in 2012 through an executive order. The Trump administration announced in September 2017 it would rescind DACA, but the policy remains in effect under a court order.
Temporary Protected Status (TPS) is given to nationals from designated countries affected by armed conflict or natural disaster. TPS holders are permitted to work and live in the US for limited times.
The Trump administration has shown a deep skepticism toward the temporary protected status program and has moved to revoke the special status afforded to thousands of immigrants from El Salvador, Haiti, Honduras and other nations.