Im said Moon may meet Trump after an inter-Korean summit but before Trump's planned summit with Kim.
North Korea's foreign minister arrived in Sweden for talks on Thursday, with a two-day visit, according to FOCUS News Agency.
"We believe in dialogue and in a political process", Wallstrom told reporters.
"We met in secret with senior North Koreans on 14 occasions", Deva said.
Sweden's embassy in Pyongyang also represents US, Canadian and Australian diplomatic interests in North Korea, with the country playing a key role in liaising diplomatic talks.
"We are a country that is militarily non-aligned and have a longstanding presence in North Korea, and with the trust we enjoy we think we can play a role".
If North Korea agrees to the talks, they would be the first North-South contact since a South Korean delegation returned from a meeting with North Korean leader Kim Jong Un this month and a chance for North Korea to break its silence on promised engagements with the South and the United States.
Meanwhile, the top diplomat is also scheduled to have a meeting with Secretary of Commerce Wilbur Ross, other government officials added, referring to Seoul's efforts to counter the U.S.'s recent decision to impose heavy tariffs on steel imports, including those from South Korea.
Foreign Minister Kang Kyung-wha told reporters before leaving for the US that she will do her best to prevent any possible disruptions in communication between the allies, a concern that has been spawned by President Donald Trump's recent firing of Secretary of State Rex Tillerson.
Are economic sanctions on North Korea effective?
However, Hoare said he wasn't sure Kim would travel to a European country, where there might be attempts to arrest him.
Trump has agreed to meet Kim by May. As the USA has no North Korean consulate, Sweden has previously stood in as its representative.
He said he did not expect the announcement of a date or location for a Trump-Kim meeting.
The closest contact Pyongyang has had with a USA administration came in 2000, when then-President Bill Clinton's Secretary of State, Madeleine Albright, visited the country to lay the groundwork for a mooted meeting between the countries' leaders.
Additionally, Kim expressed his willingness to hold talks with the United States and Trump, as well as to suspend all nuclear tests and missile launches during the negotiations.
The diplomatic wheels started turning rapidly at the beginning of the year, when the two Koreas worked to bring a handful of athletes from the North to compete in the Winter Olympics in South Korea.
It followed a year of heated rhetoric between North Korea and the USA, and growing global concern that the hostilities might escalate into military confrontation.