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 (£17.6bn) in funds for a wall on the Mexican border.
Democratic leader Chuck Schumer this week vowed to oppose funding a wall.
The details emerged in a conference call on Thursday between White House policy chief Stephen Miller and Republican congressional aides, report US media.
The plan sets out a 10-12-year path to citizenship for 1.8 million people.
This includes some 700,000 so-called Dreamers, immigrants who illegally entered the US as children and were protected from deportation under the Obama-era Deferred Action for Childhood Arrivals (Daca).
The other 1.1 million would be immigrants who did not apply for Daca but are eligible for the programme.
The White House blueprint also seeks to end two other initiatives often criticised by President Donald Trump.
It proposes to curtail so-called chain migration, permitting US residents only to get visas for their spouse and children, not for extended family members.
The White House also wants to scrap the diversity visa lottery, under which 50,000 people from around the world every year win Green Cards at random.
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 an “incentive” for so-called Dreamers to work hard and “do a great job”. (Courtesy BBC)