The presumptive GOP nominee made the comments in an interview with Reuters
on Tuesday, the news service reported. Trump said he would talk to Kim to try to stop the country's nuclear program.
"I would speak to him, I would have no problem speaking to him," Trump said.
But he also turned to one of his frequent talking points on North Korea -- that he would pressure China to put more pressure on North Korea to change its ways.
"At the same time I would put a lot of pressure on China because economically we have tremendous power over China," he said in the wide-ranging interview.
A senior South Korean Foreign Ministry official told CNN the South Korean government didn't think it was "appropriate" to weigh in on a U.S. presidential candidate's campaign trail comments, but added:
"Both the Republic of Korea and the United States are firm in their position that the issue of North Korean denuclearization should be the priority in any dialogue with North Korea.
"North Korea should stop making threats and provocations and show sincere willingness to denuclearize," the spokesperson, who was not named, said.
China is one of the few countries that engages with North Korea and is its only major backer. The Obama administration has pressured China to do more on its neighbor, but has stopped short of using economic leverage for fear of the consequences.
The comments represent a sharp turn from the way the U.S. currently approaches Pyongyang. The U.S. has no formal diplomatic relations with the country and engages through the Swedish embassy when necessary.
The Democratic People's Republic of Korea has also been hit with some of the most comprehensive sanctions of any nation in the world, and the U.S. has expressed strong condemnations of the nation's track record on human rights abuses, ballistic missile launches and nuclear ambitions.
Earlier this year, Trump referred to Kim as "like a maniac" as well as saying, "you gotta give him credit" for his ruthlessness in eliminating political enemies.
"I mean this guy doesn't play games," Trump said at a campaign rally in Ottumwa, Iowa, in January. "And we can't play games with him."
The Trump campaign did not immediately respond to a request for further comment.
Sen. Jeff Sessions, R-Alabama, the chairman of Trump's national security advisers, said it did not concern him greatly to hear Trump open the door to direct talks with Kim, citing Trump's experience as a businessman.
"One of the things I think Donald Trump understands is power and opportunity," Sessions said in an interview with CNN's Wolf Blitzer on "The Situation Room" Tuesday. "You just have to be very careful about that."
Sessions said Trump had not discussed the idea with him, and characterized it as opening up the possibility of talks, and not a firm policy.
"I believe there's nobody that's run for president in years who understands how to negotiate more effectively than Donald Trump and I do believe he will not be disadvantaged by Kim Jong Il (Un) or anybody in North Korea," Sessions said. "I think it's unlikely that a good result would come out of it, but to attempt something like that may be worth the effort."
Former New Mexico Gov. Bill Richardson, a former North Korea negotiator cast doubt on Trump's plans to talk with Kim.
"A one-on-one with Donald Trump I don't think is going to solve the problem," Richardson told CNN, adding later, that Trump's plan is "not going to work, that's not diplomacy, that's reality TV."
Then-candidate Barack Obama was criticized by Republicans during his 2008 presidential campaign for saying he would meet without precondition with Iranian leaders to discuss their nuclear ambitions.
Though there have been talks between North Korea and five other major world and Asian powers about the nuclear program for years, they have never risen to the presidential level and have not resulted in much success.
Emissaries have also traveled to the country to rescue detained Americans in the totalitarian country.
Former President Bill Clinton did travel to North Korea in 2009 and met with Kim's father, Kim Jong Il, to secure the release of detained American journalists Euna Lee and Laura Ling.
Obama himself also famously campaigned in 2008 on being willing to talk to leaders of U.S. enemies. He has followed up by shaking hands with Cuba's Raul Castro and spoken with Iranian President Hassan Rouhani. But his administration has not followed suit with North Korea and in fact deepened the isolation of the nation.
Trump's likely general election opponent, Hillary Clinton, was quick to jump on the remarks, putting out a statement from her top foreign policy adviser slamming Trump.
"Let me get this straight: Donald Trump insults the leader of our closest ally, then turns around and says he'd love to talk to Kim Jong Un?" Jake Sullivan said. "His approach to foreign policy makes no sense for the rest of us."