The release of the three Korean-Americans is under discussion through multiple channels more than a week after President Donald Trump agreed to meet the North's Kim Jong-Un, the reports said.
Pyongyang has yet to confirm it even made the US summit offer – relayed by Seoul envoys who had met Kim in Pyongyang – but South Korea said he had “given his word” about his commitment to denuclearization.
Trump's stunning announcement has triggered a race to set a credible agenda for what would be historic talks between the two leaders.
Seoul-based MBC TV station reported on Sunday that Pyongyang and Washington had “practically reached” a final agreement on the release of US citizens Kim Hak-song, Kim Sang-duk and Kim Dong-chul.
“They are hammering out details over the timing of the release,” it quoted a South Korean diplomatic source as saying.
The negotiation was held through the North's mission to the United Nations and the US State Department – an unofficial avenue of communication dubbed the “New York channel”, the source said.
CNN said the prisoners' release was also discussed at three-day talks in Stockholm between the North's Foreign Minister Ri Yong-Ho and Swedish counterpart Margot Wallström that ended on Saturday.
Sweden representes Washington's interests in the North. It raised the issue of American detainees to “move things in the right direction”, CNN quoted one source as saying.
READ ALSO: What exactly is Sweden doing in North Korea?
Kim Dong-chul, a South Korea-born American pastor, has been detained by the North since 2015 when he was arrested for spying. He was sentenced to 10 years' hard labour in 2016.
Kim Hak-song and Kim Sang-duk – or Tony Kim – were both working at the Pyongyang University of Science and Technology, founded by evangelical Christians from overseas, when they were detained last year on suspicion of “hostile acts”.
Reports of their possible release come amid a flurry of diplomatic activities involving Pyongyang and Washington along with Seoul and other US allies.
During a visit to Pyongyang by Seoul's envoys earlier this month, Kim reportedly offered to meet Trump, with the US president subsequently agreeing to talks by May. No specific time or venue has been set.
Kim also agreed to hold a summit with South Korean President Moon Jae-in next month – the third ever between the two Koreas – according to the envoys. And he reportedly offered to consider abandoning his nuclear weapons in exchange for US security guarantees.
South Korean Foreign Minister Kang Kyung-wha said in an interviewed aired on Sunday that Kim was “taking stock” after Trump's surprise decision to accept the invitation, but that a channel of communication had been established.
She said Kim had “given his word” on his commitment to denuclearization.
“But the significance of his word is quite, quite weighty in the sense that this is the first time that the words came directly from the North Korean supreme leader himself, and that has never been done before,” Kang told CBS's “Face the Nation”.
Nothing has been offered to the North Koreans to engage in negotiations, she said.
The Stockholm talks overlapped with another meeting between the national security advisers of the US, South Korea and Japan.
US National Security Advisor H.R. McMaster, the South's Chung Eui-yong and Japan's Shotaro Yachi met in San Francisco over the weekend and vowed “close policy coordination” for the weeks ahead, Seoul's presidential office said.
They agreed that peace on the Korean peninsula hinges on the success of the two planned summits, vowing “not to repeat the failure of the past”, it said in an apparent reference to previous botched nuclear disarmament negotiations with the North.
Also on Sunday a senior North Korean diplomat arrived in Finland for talks on peninsula issues with former officials and academics from the US and South Korea.
The sudden rapprochement comes months after the North staged its most powerful nuclear test and test-fired missiles capable of reaching the US mainland.
Kim and Trump traded colourful threats of war and personal insults, which heightened global concerns of another conflict on the peninsula once reduced to ruin by the 1950-53 Korean War.