Such a meeting would mark a significant change of US policy towards the politically isolated regime.
Democratic front-runner Hillary Clinton decried Mr Trump`s "bizarre fascination with foreign strongmen".
The statement, delivered by one of her aides, added that Mr Trump`s foreign policy "made no sense".
In a separate interview Mr Trump said he "absolutely had regrets" about his nine-month campaign, but that if had not conducted himself in the way he had, he would not have been successful.
Trump could visit UK before US elections.
AzVision.az has also learned that Mr Trump could visit the UK before the presidential election in November.
Diplomats expect his visit to the UK could happen after he formally becomes the Republican party candidate at a convention in July.
Earlier this week Mr Trump said "it looks like we`re not going to have a very good relationship" with the UK.
British Prime Minister David Cameron and new London Mayor Sadiq Khan have harshly criticised Mr Trump`s proposed ban on Muslims coming to the US.
Pressure on China
Mr Trump`s comments about North Korea came in an interview with Reuters news agency late on Tuesday, in which he also expressed disapproval of Russian President Vladimir Putin`s military actions in eastern Ukraine.
Mr Putin is a figure who Mr Trump has previously said he respects.
On the subject of North Korea, the New York property developer said he would pursue face-to-face talks and added that he would also put pressure on China, as North Korea`s only major ally.
"I would put a lot of pressure on China because economically we have tremendous power over China. People don`t realise that," he said.
"China can solve that problem with one meeting or one phone call."
Following Mr Trump`s comments, South Korea`s Yonhap news agency quoted China`s foreign ministry spokesman Hong Lei as saying that Beijing "supports direct dialogue and communication between the US and North Korea", adding: "We think this is a very conducive thing to do."
Trump follows Obama?
The South Korean media hang on Mr Trump`s every word - but don`t then fly into spasms of high emotion. They cover the quotes - colourful as they are - but generally don`t react beyond reportage. Politicians, too, are observing but not speaking. "Bemusement" might be the best way to describe the reaction.
After all, Barack Obama said before he was first elected, that he too would be prepared to meet the North Korean leader of the time (Kim Jong-un`s father, Kim Jong-il) face-to-face.
It`s true that Mr Obama`s promise was nine years ago and North Korea was not so far down the path to getting a nuclear arsenal. And Mr Trump has not been so cool in his language.
He recently called Kim Jong-un a "maniac" but then added what sounded like a compliment at the way the North Korean leader had consolidated his power: "How many young guys - he was like 26 or 25 when his father died - take over these tough generals, and all of a sudden... he goes in, he takes over, and he`s the boss.
"It`s incredible. He wiped out the uncle, he wiped out this one, that one. I mean this guy doesn`t play games. And we can`t play games with him."
North Korea first tested nuclear weapons in 2006, in breach of international agreements, and has made repeated threats of nuclear strikes against South Korea and the US.
Currently, any contact with the US happens between officials, not at a presidential level. The nations have no formal diplomatic relations.
Last month, Mr Trump suggested the US should stop preventing its allies Japan and South Korea from obtaining nuclear weapons, directly contradicting long-standing US policy on non-proliferation.
In the Reuters interview, Mr Trump also called for a renegotiation of the Paris climate agreement, in which more than 170 countries pledged to reduce carbon emissions.
And he said he would dismantle most of the Dodd-Frank financial regulations if he were elected president.
The Obama administration passed the regulations in 2010 to reduce risks to the US financial system and prevent a recurrence of the 2008 crisis.
`Bimbo` comment
Mr Trump was also reunited with his old adversary, Fox News presenter Megyn Kelly, with whom he has had a months-long feud that began after a TV debate in August.
In the Fox News interview, she returned to its source - a question about his attitude to women.
She asked him why he had frequently tweeted or re-tweeted insults about her, including calling her a "bimbo".
Mr Trump said he did "pretty well with real tweets" but that "the re-tweet is really more of a killer", adding he "could have done without`` his re-tweet of a post mocking the appearance of Heidi Cruz, wife of former campaign rival, Ted Cruz.
Ms Kelly also asked if Mr Trump had any regrets about his nine-month campaign.
He said: "Absolutely, I have regrets... I could have done certain things differently, I could have maybe used different language but overall I have to be very happy with the outcome."
He added: "If I didn`t conduct myself in the way I`ve done, I don`t think I would have been successful."
Mr Trump won the Republican primary in Oregon on Tuesday, where Bernie Sanders emerged victorious in the Democratic race.
The Kentucky primary, which was Democratic-only, was too close to call but Hillary Clinton declared victory with most of the votes counted.
