American citizens Kim Hak-song, Kim Sang-duk, and Kim Dong Chul are being held by North Korean government.
North Korean Foreign Minister Ri Yong Ho is in Stockholm for talks with his Swedish counterpart. Sources tell CNN that Sweden "engaged heavily" in the issue of the American detainees, and since Sweden is a protective power for the US, it also represents the country's interest in all talks with North Korea.
"Any movement on the issue of these detainees would be a huge deal for the US," one source with knowledge of negotiations said, adding that Sweden did not issue any ultimatum during the weekend talks; rather, they brought it up as something that would "move things in the right direction".
Sources said the issue has been at the center of discussions for some time, both at previous low-level meetings and during North Korean Deputy Foreign Minister Han Song Ryol's visit to Sweden in January.
Kim Hak-song -- an ethnic Korean born in Jilin, China, and educated at a university in California -- was detained last May, North Korean state media reported at the time. The previous month, Kim Sang-duk had also been detained while trying to fly out of Pyongyang International Airport.
Kim Dong Chul is a South Korean-born American citizen who had been living in China when he was detained.
Kim Dong Chul told CNN's Will Ripley that he had been arrested after spying on behalf of "South Korean conservative elements." His claims were made in the presence of North Korean officials, and CNN cannot determine whether they were made under duress.
Previous US detainees
Since 2013, at least two other US citizens have also been detained for shorter periods. Merril Newman, who at the time of his October 2013 detention was an 85-year-old US veteran of the Korean War, was released two months later after a videotaped apology. American Jeffrey Fowle spent five months in detention in 2014 for allegedly leaving a Bible at a club for foreign sailors.
North Korea -- US summit
North Korea has yet to make an official comment on the proposed meeting. Trump accepted the invitation from Kim when a South Korean delegation delivered it verbally in Washington.
Should the leaders of the two nations sit down, it would be the first time that a sitting US President has met with the leader of the reclusive Asian nation.