President Moon Jae-in and U.S. President Donald Trump stand together at Cheong Wa Dae in Seoul, Sunday. Yonhap

South Korean President Moon Jae-in will have talks in Seoul with U.S. President Donald Trump on ways to reinvigorate the Korea peace process, with a three-way summit involving North Korean leader Kim Jong-un perhaps in the offing.

Moon and Trump plan to meet bilaterally at Cheong Wa Dae at 11 a.m. after Trump's meeting with a group of South Korean business leaders at a Seoul hotel.

The duo will then have an expanded meeting, joined by their key aides, over lunch that will be followed by a joint press conference.

They are expected to discuss how to resume denuclearization talks and also address pending alliance and trade issues.

It will be their first one-on-one summit since the April one at the White House.

What will happen in the afternoon is drawing keen attention as well.

Trump, Kim to meet at Panmunjom 2019-06-30 09:24  |  North Korea
Trump announced that he will travel to the inter-Korean border, known as the Demilitarized Zone (DMZ), before leaving Korea after his two-day stay here. He flew to South Korea from Japan on Saturday evening and soon attended a Cheong Wa Dae welcome dinner hosted by Moon.

"Today I will visit with, and speak to, our Troops - and also go to the DMZ (long planned)," he tweeted Sunday morning.

At the dinner, Trump said he "toasted" a "new Trade Deal." He was apparently referring to the revision of a bilateral free trade agreement.

Trump has proposed a "handshake" meeting with Kim at the DMZ and said Pyongyang was "receptive" to the offer.

In response to Trump's Twitter invitation for Kim, North Korea's Vice Foreign Minister Choe Son-hui called in a "very interesting" suggestion. If realized, she said in a statement, it would serve as "another meaningful occasion in further deepening the personal relations between the two leaders and advancing the bilateral relations."

It's uncertain whether Kim will accept the offer for a third meeting with Trump.

Moon may travel to the DMZ together with Trump, while Cheong Wa Dae has not confirmed any related schedule.

Moon's aides just said the president is making preparations for every possible scenario.

On a potential three-way DMZ summit, Trump told reporters shortly before the Friday dinner: "We're gonna see. We are working things out right now."

Trump is scheduled to depart from Korea in the afternoon, but there's a possibility that he will change the schedule. (Yonhap)