The White House has outlined an immigration plan that would allow 1.8 million people to become US citizens in exchange for funding for a border wall.
The framework was described by a senior Trump aide in a conference call to Republicans ahead of legislative negotiations with Democrats.
The proposed bill, to be unveiled on Monday, requests $25bn ($NZ34bn) in funds for a wall on the Mexican border.
Democratic leader Chuck Schumer this week vowed to oppose funding the wall.
What is the plan?
Under the White House proposal, US residents would only be able to sponsor the visas of spouses and children, rather than extended family members.
The diversity visa lottery, under which 50,000 people win Green Cards annually, would be scrapped entirely. Mr Trump has frequently criticised that programme.
The details emerged in a conference call on Thursday between White House policy chief Stephen Miller and Republican aides and journalists.
Mr Miller said the 1.8 million figure includes some 700,000 people who illegally entered the US as children.
These people were protected from deportation under the the Obama-era Deferred Action for Childhood Arrivals (Daca).
Mr Miller said a million others who did not apply for Daca but otherwise met its requirements could also be offered a path to citizenship under the White House plan.\
Why is Daca important?
Mr Trump cancelled the Obama-era programme in September and gave Congress a March deadline to come up with a new plan.
The president has so far rejected bipartisan proposals that have been presented to him.
Congress' failure to secure a deal on immigration triggered a brief shutdown of the federal government over the weekend.
On Wednesday, Mr Trump said he was optimistic that a deal on immigration would be reached that included keeping the so-called Dreamers in the country.
He added that it was "incentive" for so-called Dreamers to work hard and "do a great job".