The two countries were looking at five potential venues for the summit, "but it is not in the United States", Trump told reporters at Mar-a-Lago where he was hosting Japanese Prime Minister Shinzo Abe.
"We've also started talking to North Korea directly.We have had direct talks at very high levels -- extremely high levels -- with North Korea," Trump said before a restricted bilateral meeting with Abe.
"I really believe there's a lot of goodwill. A lot of good things are happening.We'll see what happens.As I always say, we'll see what happens.Because ultimately, it's the end result that counts, not the fact that we're thinking about having a meeting or having a meeting," he said.
Asked about the location of the potential venues, Trump confirmed that they were outside the US.
"We have not picked a site yet, but we've picked five sites where it's potentially going to be. We'll let you know fairly soon. Let's see what happens.We'll either have a very good meeting or we won't have a good meeting. Maybe we won't even have a meeting at all depending on what's going in," he said.
The US president said irrespective of whether the meeting happens or not, there was mutual respect for each other between the two countries.
"I look forward to meeting with Kim Jong-un. And hopefully that will be a success. Maybe it will be, and maybe it won't be. We don't know. But we will see what happens. But I can say this: They do respect us. We are respectful of them. We are going to see what happens," Trump said.
In his remarks, Abe said prior to the small group discussion at the one-on-one session, the two leaders already had a very in-depth discussion focusing on the issue of North Korea and also the economic issues.
"On those two points, we actually successfully forged a mutual understanding.So, I'm very happy to see the outcome of our one-on-one discussion," he said.
Abe said the planned meeting between South Korea and North Korea was made possible with the help of Trump who successfully pressured Pyongyang into softening its stance.
"Since the Pyeongchang Winter Olympic Games in South Korea, we have observed major change in terms of North Korea's behaviour.Background of this change is Donald's (Trump)unwavering conviction, as well as the determination that you demonstrated in addressing the issue of North Korea. So your stance made it possible to achieve this major change," he said.
"As a matter of fact, the US has the overwhelming military power in the world. By using this strength, you have been effectively applying the overwhelming level of pressure against North Korea. And this, actually, successfully led to the outcome that we have already observed," Abe said.
The Japanese prime minister expressed hope that the US-North Korea summit meeting yield tangible progress toward resolving a wide range of issues, from nuclear issues, missile issues to the abductions issue.
"So this will be a historic meeting, and I certainly hope that there will be progress on these fronts," he said.
Trump said he will bring up the abductees.
The US President also thanked the Chinese President Xi Jinping for playing a "constructive" role on the issue of North Korea.
"He's been incredibly generous.They have never been this way with the United States.I think they have more respect for us, perhaps our leadership, but for us than they've ever had before," he said.
"President Xi has been very strong on the border, much stronger than anyone thought they would be.I'd like them to be stronger on the border.But he has been at a level that nobody ever expected.The goods coming into North Korea have been cut down very substantially.As you know, 93 per cent of the goods coming into North Korea come through China, come through the border," Trump said.