Trump’s venue suggestions came during a news conference with the Nigerian President on Monday.
Panmunjom is considered a neutral location between the two Korean nations; the village in the border area between them where the inter-Korean summit occurred last Friday.
Tuesday, an official from South Korea's presidential office told reporters that South Korean president Moon Jae-in and President Trump talked about the pros and cons of holding a summit at Panmunjom.
"It’s not that President Moon suggested [Panmunjom] first. It just came out naturally when the two leaders were talking about where would be a good venue," the official said.
The South Korean government made clear that "nothing" has been decided regarding the time and place of the U.S.-North Korea summit, pushing back on a CNN report that Moon had persuaded Kim to hold the meeting at the DMZ.
"For now, nothing has been decided and we are waiting for the decision-makers to make their final decision. I hope [we] don't go too far ahead," Yoon Young-chan, Senior Secretary to the President for Public Communication told ABC News Tuesday.
South Korea’s foreign ministry stayed on the same page with the presidential office that summit venue decision was an open question, but added it would be meaningful for Panmunjom to host US-North Korea summit.
"There is nothing we can confirm on whether Panmunjom will be hosting,” Foreign Ministry spokesperson Noh Kyu-duk said during a press briefing Tuesday. "But if Panmunjom, which symbolizes division, become host, it will have significant meaning as a new milestone for peace."
Meanwhile, South Korea’s military began removing propaganda speakers installed at the military demarcation line facing the North on Tuesday -- the first action to follow up the deal between North and South Korea, just four days after the inter-Korean summit.
North Korea’s military also took down their propaganda speakers, according to Yonhap’s report citing South Korea’s military official, the same day.
A joint statement issued by the two nations after the inter-Korean said both sides had agreed to cease all hostile acts against each other.