Moon said earlier this week he wants to meet the North's leader regardless of the venue or the format as part of efforts to help break the deadlock in nuclear talks between the North and the United States. The North has not responded to the offer yet.
But the unification minister said he was positive the North will respond.
"As you can see, the two leaders have continued to confirm the trust they have in each other. So (the response) will very likely come," the minister told reporters after a meeting with the head of the Jogye Order of Korean Buddhism, Ven. Wonhaeng, in Seoul.
South Korea has been eager to broker the deadlocked nuclear negotiations between Washington and Pyongyang after Trump and Kim's second summit in Hanoi collapsed without an agreement.
Pyongyang, however, has been increasingly voicing its displeasure at both Seoul and Washington, calling on South Korea to effectively take the North's side and demanding the US replace its chief negotiator, Secretary of State Mike Pompeo, for the talks to proceed.
Moon and Kim held three inter-Korean summits last year, with their latest meeting in Pyongyang in September. (Yonhap)