US officials have shrugged off North Korea's weapons tests and end-of-the-year ultimatum.
Working-level talks broke down after a February summit between Trump and Kim in Hanoi, Vietnam, ended in no deal.
Analysts say he could pass him a message from Mr Kim about the nuclear negotiations.
President Trump's interview with a team of newshounds from Time journal took a unexpected flip when he made a commentary about penal advanced time for a journalist.
"Did Trump indicate a willingness to moderate the USA negotiating position (good)?"
Mr Trump rebuked the photographer within the Oval Jam of enterprise after he used to be warned by an aide now no longer to resolve on a characterize, according to Time's transcript. Vipin Narang, a North Korea expert and professor of worldwide relations at MIT, wrote on Twitter.
The official Trump Facebook and Twitter accounts posted the video yesterday which showed a Time magazine front cover about "How Trumpism outlasts Trump", featuring campaign signs for Trump 2024, Trump 2028 and so on.
"Something is up as Trump seems to have struck the right chord" with Kim, the former State Department nonproliferation and East Asia desk official wrote on Twitter.
The US is demanding that North Korea abandon its nuclear weapons entirely before global sanctions are lifted. North Korea is seeking a step-by-step approach in which moves toward denuclearization are matched by concessions from the USA, notably a relaxation of the sanctions.
China backs what it calls a "suspension for suspension" proposal.
"The government views the exchange of letters between the U.S. and North Korean leaders positively for carrying on the momentum of dialogue between the two", presidential spokesperson Koh Min-jung told reporters in a text message.
"So this became once written by Kim Jong-un".
Such an agreement, which would let the North keep its current arsenal, would eventually confer upon the country de facto, if not outright, status as a nuclear power, he said.
At quite a lot of functions throughout the interview, Mr Trump requested to talk off-the-yarn, together with within the moments after exhibiting the Time reporters a letter he acknowledged used to be from the leader of North Korea.