That amount is far less than Trump has demanded. But if accepted, the deal would avert another chaotic standoff in which Trump has threatened to cut budgets from swaths of government this Friday.
Senator Richard Shelby, a key Republican negotiator, told reporters an agreement in principle had been reached between Republican and Democratic lawmakers.
Senior congressional aides told AFP the agreement included $1.375 billion in funding for a wall on the US-Mexico border - a key campaign promise of Trump, who had demanded $5.7 billion for his pet project.
The agreed figure would fund approximately 55 miles (89 kilometers), all to be located in the Rio Grande Valley area of south Texas, the aides said.
The deal still faces White House approval.
The news dropped just as Trump was about to climb the stage in the El Paso arena and the president, addressing a raucous crowd, said he did not have enough details to respond.
"We probably have some good news but who knows," he said. Addressing thousands of people, many wearing his red "Make America Great Again" campaign hats, Trump said: "We need the wall and it has to be built and we want to build it fast."
According to Trump, illegal immigrants pose a national security risk to the United States and can only be stopped by dramatic extensions of current barriers.
It's an argument he backs up with lurid warnings about rapists and people traffickers extending far into the American heartland - a message that critics describe as xenophobic and based on heavily manipulated data.
The border controversy is the opening battle of Trump's 2020 reelection bid and his El Paso rally gave a taste of things to come.
Trump chose the setting as a historic crossing point where he says walls have successfully halted an out-of-control influx of Mexican criminals.
"Walls save lives, walls save tremendous numbers of lives," he said.
There was a counter-message a short distance from where Trump spoke when rising Democratic star Beto O'Rourke - a possible challenger in 2020 - held his own rally.
A former congressman who excited grassroots Democrats last November with an against-the-odds near upset of Republican Senator Ted Cruz, O'Rourke is from El Paso.