"We see it as a very interesting suggestion, but we have not received an official proposal in this regard," the North's Korean Central News Agency (KCNA) cited First Vice Foreign Minister Choe Son-hui as saying.
The statement added that a meeting "would serve as another meaningful occasion in further deepening the personal relations between the two leaders and advancing the bilateral relations".
Trump's unexpected offer was made in a tweet early Saturday morning from the G20 Summit in Osaka, Japan, just hours ahead of his trip to South Korea, to visit President Moon Jae-in.
"After some very important meetings, including my meeting with President Xi of China, I will be leaving Japan for South Korea (with President Moon)," Trump tweeted.
"While there, if Chairman Kim of North Korea sees this, I would meet him at the Border/DMZ just to shake his hand and say hello."
It was expected that Trump was scheduled to visit the DMZ during his visit to Seoul this Saturday and Sunday, but the White House had assured that the President would not meet Kim there.
Trump has held two summits with the North Korean leader, the first a year ago in Singapore, where both pledged to "work toward the complete denuclearization of the Korean Peninsula".
During the second summit between held at the end of February in Hanoi, Vietnam, the leaders failed to agree on how the denuclearization process should be carried out.
Trump will arrive in Seoul on Saturday afternoon, where he plans to stay for 24 hours to meet Moon and discuss the North Korean situation.
The US President wanted to visit the DMZ during his first visit to South Korea in 2017, but ultimately he could not do so due to bad weather.
( With inputs from IANS )