At the White House on Thursday, Trump was asked by reporters if he plans to meet Kim this year and whether he has a new proposal for denuclearization negotiations with Pyongyang, reports Yonhap News Agency.
"At some point, yes," Trump said of the potential meeting.
"Certainly, (the North Koreans) want to meet. They'd like to meet. I think it's something that will happen. And we'll see, but Kim Jong-un -- I think something can happen."
"Well, we're gonna see," the President said, adding "I think that North Korea would like to meet. I think you probably have heard that".
Trump and Kim have had three meetings since June 2018 to negotiate the North's denuclearization in exchange for US sanctions relief and security guarantees.
But talks have stalled since Trump and Kim's second summit in Vietnam in February ended without a deal.
On Monday, the North's First Vice Foreign Minister Choe Son-hui said her country would be willing to resume talks later this month but demanded a new proposal acceptable to Pyongyang.
Meanwhile, South Korean President Moon Jae-in and Trump will hold summit talks in New York later this month on the sidelines of the 74th UN General Assembly session, the Presidential Palace in Seoul announced on Friday.
Besides the meeting, Moon is scheduled to deliver a keynote speech at the UN session on September 24 and also hold a series of bilateral talks with UN Secretary-General Antonio Guterres and leaders from other countries.