Asked by journalist Sharyl Attkisson, host of the "Full Measure" TV show, whether he would "ever consider sitting down with the dictator," Trump said he was holding meetings with numerous Asian leaders.
"I would sit down with anybody," he said. "I don't think it's strength or weakness, I think sitting down with people is not a bad thing.
"So I would certainly be open to doing that but we'll see where it goes, I think we're far too early."
Trump's conciliatory-sounding comment came after months of fiery rhetorical exchanges between the two leaders, prompted by a series of internationally condemned nuclear and missile tests by the North.
The North has denounced Trump as a "mentally deranged US dotard," or senile old man, and the country's ruling party newspaper Rodong Sinmun referred to him Sunday as "instable."
Trump, for his part, has mocked Kim as "Little Rocket Man" and has vowed to rain "fire and fury" down on the North if it threatens the US or its allies.
Trump's latest comment appeared to be something of a reversal from a Twitter message he sent just over a month ago, in which he said that US Secretary of State Rex Tillerson was "wasting his time" trying to negotiate with the North Korean leader.
Trump then travels to China on Wednesday, Vietnam on Friday and the Philippines on Sunday.
The interview was broadcast as a letter by the US Defense Department emerged that said the only way to locate and secure all North Korea's nuclear weapons sites would be via a US ground invasion.
The two-page document was addressed to Ted W. Lieu, a Democratic member of Congress in response to a request regarding "expected casualty assessments in a conflict with North Korea."
"The only way to 'locate and destroy -- with complete certainty -- all components of North Korea's nuclear weapons programs' is through a ground invasion" it said.
It added "a classified briefing is the best venue for a detailed discussion" of such a plan.