"I don't want to comment on it. I'm not saying I have or haven't," he said in an interview with The Wall Street Journal
published Thursday. "I just don't want to comment."
Trump's strategy with North Korea has been hot and cold. While he has expressed an openness to negotiating with North Korea, he has also promised "fire and fury" for North Korea if their nuclear program and missile tests continued and recently said his nuclear button is "bigger and more powerful" than Kim's, whom he has taken to calling "Little Rocket Man."
Trump said the stop-and-go nature to his strategy with North Korea is intentional and part of a broader goal.
"You'll see that a lot with me," he said. "And then all of the sudden somebody's my best friend. I could give you 20 examples. You could give me 30. I'm a very flexible person."
White House and National Security Council officials declined to comment on whether Trump and Kim have talked.
A senior administration official, asked if Trump has spoken to or contacted Kim, told CNN: "That's not something we would discuss but we are not aware this contact has occurred."
Trump's comments come days after representatives from North and South Korea held daylong negotiations in the demilitarized zone, where Pyongyang agreed to send a delegation to next month's Winter Olympics and to hold talks with Seoul to ease military tensions.
During his interview with The Wall Street Journal, Trump acknowledged that recent talks between the two Koreas may be an attempt to drive a wedge between South Korea and the United States.
"If I were them, I would try," he said. "The difference is I'm president, other people aren't. And I know more about wedges than any human being that's lived."
Trump previously exaggerated the nature of his relationship with Russian President Vladimir Putin.
"I got to know (Putin) very well because we were both on '60 Minutes,' we were stablemates, and we did very well that night. But, you know that," Trump said during a 2015 Republican debate.
Trump later walked those comments back.
"I never met Putin," Trump said in 2016. "I don't know who Putin is."
Putin: Kim 'won this round'
The Russian leader said, during a meeting with heads of Russian print media and news agencies, that Kim was already a "shrewd and mature politician" and that the North Korean had "obviously won this round," referring to the latest political and diplomatic developments on the Korean Peninsula.
Without directly referencing the United States or Trump, Putin said he felt Kim had outsmarted his political adversaries.
"He has a nuclear weapon, he has missiles of global reach, up to 13,000 kilometers, which can reach almost any point of the globe or at least any point of his potential enemy.
"Now he's of course interested to de-escalate and cool the situation around it. He is already a shrewd, shrewd and mature politician."
Putin added that the ultimate goal of denuclearlization could to be reached "if all the participants of the talks, including North Koreans, will be assured that their safety is possible without nuclear weapons."
No sitting US president, according to Gordon Chang, an author and expert on North Korea, has ever talked to the current Kim family ruler in North Korea.
President Jimmy Carter spoke with Kim Il Sung in 1994, but he was a former president by that point and Bill Clinton was in office. Clinton, as part of an effort to free two American journalists, met with Kim Jong Il in 2009, but Barack Obama was president at the time.