"The visit can happen anytime if North Korea sends an invitation to pope," Kim said at a news conference held at Gwangju Archdiocese in the southern city of Gwangju, Yonhap News reported.
"I saw U.S. news reports saying the pope's travel plan for next year doesn't include a trip to North Korea. But we never know. If pope wants, he can go anytime," he said.
Kim added that pope's visit can provide a "nice opportunity" for Kim because it can encourage him to "give up nuclear weapons," and sharing his pledge for denuclearization with the pope could also help other countries have faith in his promise.
Kim said that he sent a letter to U.S. President Donald Trump last week, asking him to lift economic sanctions against North Korea.
"I said I would like to see the U.S. take corresponding measures when North Korea takes steps to denuclearize its nuclear weapons and the U.S. lift economic sanctions against North Korea," he said.
South Korean President Moon Jae-in said earlier in a visit to the Vatican that Kim wants to invite Pope Francis to Pyongyang.