But Democrats dismissed the offer as non-starter, calling on Trump to re-open the government first.
Speaking from the White House, Trump said he was offering a "common sense compromise both parties should embrace."
In advance of Trump's remarks, House Speaker Nancy Pelosi said the expected proposal for ending the 29-day partial government shutdown was "a compilation of several previously rejected initiatives, each of which is unacceptable."
The California Democrat said Trump's expected offer was "not a good-faith effort" to help the immigrants and could not pass the House.
Trump said he would extend protections for young people brought to the country illegally as children, as well as for those with temporary protected status after fleeing countries affected by natural disasters or violence.
Democrats criticized the expected proposal because it didn't seem to be a permanent solution for those immigrants and because it includes money for the wall along the U.S.-Mexico border, which the party strongly opposes. Democrats also want Trump to reopen government before talks can start.