US President Donald Trump, who is expected to hold his own much-anticipated summit with Kim later, previously offered his "blessing" for the two Koreas to discuss a treaty.
Yet, for Washington and Pyongyang, there's a list of other potential goals that could be accomplished through their meeting, including a lasting agreement to end the nearly 70-year state of war on the Korean Peninsula.
One U.S. government official said privately that there has been no recent signals that the release of the hostages is imminent but added that it would be highly unlikely for Trump to meet with Kim and not secure the release of the prisoners in the same meeting.
Hundreds of thousands of Americans - civilians and military - live in Guam, South Korea and Japan and are in direct danger from North Korean attack.
In November, it said it had successfully tested a new type of intercontinental ballistic missile that could reach the whole of the continental United States. "They have not attached any conditions that the USA can not accept, such as the withdrawal of American troops from South Korea".
Senior delegations from both sides have held meetings prior to the Korean leaders' summit, sparking speculation from local media sources that the historic occasion may mark an official end to the war.
"The North Koreans did not present any conditions that the United States could not accept, such as the withdrawal of American troops in South Korea", Moon was quoted as telling media executives Thursday.
But are Trump, Kim and Moon talking about same thing when it comes to North Korea giving up its nuclear capabilities? At the meeting, Mr Kim said he was hopeful that complicated conflicts could be resolved over a single phone call with Mr Moon.
The plan was unveiled by the South's National Security Adviser, Chung Eui-yong, after he met Kim last month in Pyongyang.