The president did not give any more details on the meeting, during which he will try to craft a path toward the dictatorship giving up its nuclear and missile programs.
"I want to get peace. The main thing — we want to get peace. ... We'll see," Trump told reporters during an event at the White House. "We're setting up meetings right now and I think it's probably going to be announced over the next couple of days — location and date."
Asked later Tuesday about Trump's comments, White House press secretary Sarah Huckabee Sanders said the list of potential meeting locations has been "narrowed." She said she expects an announcement "soon."
On Friday, Kim and South Korean President Moon Jae-In met about the denuclearization of North Korea, but did not give any details about how they planned to achieve it. The pair signed a declaration saying they seek the "complete denuclearization of the Korean Peninsula."
On Saturday, Trump said he had a "long and very good talk" with Moon. In a tweet, he said "things are going very well."
The U.S., South Korea and their allies have pushed for North Korea to stop its nuclear and missile programs. They have used escalating economic sanctions to try to put pressure on Pyongyang.
Trump has repeatedly pushed China, which has supplied a key economic lifeline for North Korea, to do more to pressure the dictatorship.
Trump said that, regardless of where the meeting takes place, he wants to achieve peace.
"The main thing is to get it done. I want to get it done," he said.