"I think that what the definition of a wall is, is something that we all need to have a serious conversation" about, White House legislative affairs director Marc Short said on CNN's "The Situation Room."
Short said, "in some cases," it would be a kind of fencing.
"It is a myriad of different structures," Short said.
He said that the White House would outline all of its immigration priorities, including ramped-up domestic enforcement and border security, in the next seven to 10 days.
During the campaign, Trump promised a wall that Mexico would pay for along the border between the two nations. Months into the job, Mexico is continuing to declare it will not pay for the wall and appropriations from the US Congress have not come through, either.
The Department of Homeland Security announced
at the end of August the vendors it selected to build prototypes for Trump's proposed wall.
Trump claimed this week that the wall was already under construction -- if one considered the wall to be "new renovation of old and existing fences and walls."
Some of Trump's most hard-line supporters have expressed dismay at Trump's shifting rhetoric on immigration and the wall. On Thursday, Iowa Republican Rep. Steve King said
he believed a failure for Trump to make his campaign promises a reality would undermine his reelection chances, and said border security alone did not equate to a wall.
"The American people know what a wall is," King said.
As for Mexico paying for the border structure, Short maintained Friday that Trump would make it happen.
"The President is going to deliver on his promises," Short said. "I've doubted the President before and been proven wrong. I suspect that he's going to make sure that that wall is built and that Mexico will pay for it."
Short said the White House is talking to Republican offices on Capitol Hill as Congress considers potential protections for young undocumented immigrants whom the government granted relief from the threat of deportation under the Deferred Action for Childhood Arrivals (DACA) program.
He said he was in the room when Trump dined earlier this week with House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer. After the dinner, the two Democrats announced a potential agreement on DACA that excluded Trump's wall.
Short denied there was a deal and instead referred to the dinner as the "beginning of a conversation" in which Trump was sincere in his desire to protect DACA recipients. He said Trump wanted a legislative fix.
"He feels that these are 800,000 people who came to the United States, no fault of their own, who are productive and working in American society," Short said. "He wants to find a solution for them."
The administration is not currently backing any deal that offers Dreamers a pathway to citizenship, he added, although he would not rule it out.
"I think that it is for the President to make the final determination in that negotiation," Short said.