North Korean intelligence officials along with their American colleagues have met several times to determine where talks should be held, considering the Mongolian capital Ulaanbaatar as an option, according to CNN.
Central Intelligence Agency director Mike Pompeo and the CIA team have been operating through intelligence back-channels to make arrangements for the summit.
The North Koreans are insisting on having the meeting in their capital, Pyongyang, although it is unclear whether the White House wants to hold the talks there, the sources said.
The CIA has refused to comment on the meeting, according to an official representative.
Earlier in March, Kim spoke about his intention to normalize relations with Washington during a meeting with a South Korean delegation in Pyongyang, noting that his final goal was to sign a peace agreement with the US and establish diplomatic ties, possibly including the opening of a US Embassy in Pyongyang.
Trump has accepted the invitation to meet with Kim by the end of May following months of heightened tensions and exchanges of frequent military threats between the two leaders.
The US President later stated that he expected "tremendous success" in solving the North Korean issue, saying that he expected Pyongyang to cease its ballistic missile and nuclear tests, as well as ultimately denuclearize completely.