There is a "strong possibility" the summit will be held at the site, with some events possibly scheduled on the northern side of the military demarcation line separating the two countries, according to an official with deep knowledge of North Korea's thinking on the matter.
The venue makes the most sense logistically for Kim, the source said, because media facilities and equipment are already in place, which could the allow the summit to take place "in late May."
Traveling to the northern side of the DMZ would also provide a historic opportunity for Trump, the source said, adding that Moon may be involved in the summit in some capacity.
The idea of meeting at the DMZ wasn't a complete surprise to aides since Trump has been talking about it all weekend and raised it in his Sunday phone call with Moon, a senior US official and a person familiar with the conversations told CNN.
Trump loved the images from the inter-Korean summit and the fact the entire meeting was televised, those sources said.
Speaking to reporters Monday, Trump said he was enthusiastic about the idea of holding the summit in the DMZ. "There's something I like about it, because you're there, if things work out, there's a great celebration to be had on the site, not in a third party country," he said.
Millions watched Moon's meeting with Kim last Friday, the first meeting between two leaders of North and South Korea in a decade.
Cameras followed the leaders' movements throughout the day, from Moon's departure from Seoul to the moment Kim crossed the demarcation line into the south -- and encouraged Moon to cross to the North.
US officials are still arguing for Singapore as a possible location for the talks, telling Trump it presents a more neutral option, the sources said.
But one senior official conceded the symbolism wouldn't be there, and noted there are still logistical considerations to worry about with Singapore, a city-state south of Malaysia.
Concerns remain inside the administration that Trump may be too eager for a deal. Those same skeptics worry holding the meeting at the DMZ will appear conciliatory toward Kim.
As he has said in public, Trump remains insistent he will not be played as the two seek to end the standoff over North Korea's nuclear weapons program.