On a flight to Iowa, while campaigning for the mid-term polls to be held on November 6, Trump told reporters: "I just can't leave now."
Earlier on Tuesday in a media interaction at the Oval Office, he said the venue of his second meeting with Kim has been narrowed down to "three or four" locations...timing won't be too far away".
Asked if his Mar-a-Lago estate is an option, Trump smiled and said that Kim would "probably like that. I'd like that, too. I think it would be good. But we'll see."
The President though did not specify whether any of the places under consideration are in the US. He said that as the process would go on, "eventually we're going to have lots of meetings on US soil and on their (North Korea's) soil by the way. That's a two-way street".
US Secretary of State Mike Pompeo met Kim this Sunday in Pyongyang to prepare the second summit between Trump and the North Korean leader, and let it be known that this meeting will take place "as soon as possible."
Pompeo said that significant progress has been made toward moving forward with denuclearization talks, but didn't wish to give any details at the time.
US Secretary of State Mike Pompeo had "good talks" with Kim during his Sunday trip to Pyongyang, Trump said, adding that progress had been made on denuclearization of the Korean Peninsula.
"While there's still a long way to go and much work to do, we can now see a path to where we'll achieve the ultimate goal," Pompeo had said.
The first-ever Pyongyang-Washington summit was held in Singapore on June 12.
According to a joint statement signed by Trump and Kim, the US would provide a security guarantee to North Korea in return for Pyongyang's commitment to denuclearizing the Korean Peninsula.
(With inputs from agencies.)