The potential approach was confirmed Thursday by two congressional officials and a senior transition official with knowledge of the discussions; all spoke on condition of anonymity because they were not authorized to discuss the matter publicly. The officials emphasized that no final decisions had been made.
The approach could come as a surprise to some but could also stave off a legislative fight that Trump might lose if he tried to get Congress to pass a stand-alone bill authorizing the kind of border wall he promised during the campaign.
It's not clear how much could be done along the 2,000-mile border without additional actions by Congress. Lawmakers passed the Secure Fence Act of 2006, but most of those 700 miles have already been built.
Some areas are in much better shape than others, though, and long stretches are made up of fencing that stops vehicles but not pedestrians.
But whatever steps might be taken without Congress' approval would be likely to fall short of the extravagant new wall on the border that Trump repeatedly said Mexico would pay for during the campaign for the White House.
And despite Congress' involvement in approving any spending, such an approach might also open Trump to charges of circumventing the House and the Senate to take unilateral actions, something he repeatedly criticized President Barack Obama for doing.
A spending bill including money for border construction could also provoke a legislative showdown given potential opposition from Senate Democrats.
Still, several lawmakers and congressional officials said the administration could have significant flexibility in taking additional steps without Congress' approval.
"There's a lot of things that can be done within current law," said Rep. Mario Diaz-Balart, R-Fla., a longtime proponent of comprehensive immigration reform, though he emphasized that a lasting solution on immigration would take action by Congress. "You cannot minimize the potential impact of the administration doing what they can do under the law," he said.
However, some immigration hard-liners have already expressed the desire to see Congress take a vote given how prominent the wall was during Trump's presidential campaign, and their desire to act on the issue.
Trump's vow to build an impenetrable, concrete wall along the southern border was his signature campaign proposal. "Build the wall!" supporters would chant at his rallies. "Who's going to pay for it?" Trump would ask them. "Mexico!" Trump often promised the wall would be built of hardened concrete, rebar and steel as tall as his venues' ceilings, and would feature a "big, beautiful door" to allow legal immigrants to enter.
Most experts viewed such promises as unrealistic and impractical, and Trump himself sometimes allowed that the wall would not need to span the entire length of the border, thanks to natural barriers like rivers. After winning the election, he said he'd be open to stretches of fencing.
—CNBC contributed to this report.