He said the details of the summit would be announced soon, with the White House saying it could take place this month as long as North Korea makes specific concessions.
Speaking to reporters, Mr Trump said “a lot of things have happened” with regards to US citizens reportedly being held in North Korea.
“We’re having very substantive talks with North Korea and a lot of things have already happened with respect to the (US) hostages,” he said. “I think you’re going to see very good things.”
The US President also said the prospect of withdrawing troops from South Korea was “not on the table”.
It comes as the UN aviation agency, the International Civil Aviation Organisation (ICAO), said North Korea had requested new air routes to South Korea and that the regime’s request was “under consideration”.
Speaking about the highly anticipated summit, Mr Trump said: “We now have a date and we have a location. We’ll be announcing it soon.”
He suggested he was looking for the meeting – the first time leaders of the two countries have met since the Korean War – to be held at the demilitarised zone between the two Koreas.
It is where Kim Jong Un met South Korea’s Moon Jae-in last week.
The latest development follows vice president Mike Pence postponing a planned trip to Brazil at the end of May to free up resources for President Trump’s North Korea summit.
In March, Mr Trump hailed the “great progress” made with North Korea after he said he agreed to meet with Kim Jong Un by May this year.
He had confirmed on Twitter that a meeting was being planned, despite the two leaders trading insults for months and economic sanctions on North Korea being ramped up in response to its nuclear weapons programme.
Mr Trump previously threatened “fire and fury” in response to threats from North Korea. Mr Trump also referred to the North Korean leader as “little rocket man”.
Since then, North and South Korea have agreed to a “complete denuclearisation” of their peninsula in historic talks between the two countries.
A joint statement from the Korean leaders said they had confirmed their goal of achieving “a nuclear-free Korean peninsula through complete denuclearisation”.