It would be his first trip to South Korea in six months.
Trump and Kim met for the first time in 2018 in Singapore, raising hopes of an agreement to get Pyongyang to give up its nuclear weapons programme.
Inter-Korean relations have been in deep freeze following the collapse of a summit between Mr Kim and United States President Donald Trump a year ago over what the nuclear-armed North would be willing to give up in exchange for a loosening of sanctions.
In a virtual summit with EU Council President Charles Michel and European Commission President Ursula von der Leyen the previous day, Moon reaffirmed his resolve to strive "with patience" to maintain the momentum of dialogue involving the US and the two Koreas, the official added.
The moves against the activists have invited criticism that President Moon Jae-in's liberal government is sacrificing democratic principles to try to fix deteriorating ties with North Korea.
Abrams then stressed the spirit of "fight tonight", referring to the highest defense readiness of the combined forces should be on against any outside aggression, mainly from the nuclear-armed North Korea.
Moon's office had conveyed such views to Washington and the officials there are making efforts, the official said.
Sources close to the two governments have told NHK that Deputy Secretary of State Stephen Biegun is expected to meet with Lee Do-hoon, Seoul's special representative for Korean Peninsula peace and security affairs.
"I think it's probably unlikely between now and the USA election", Biegun told a forum, adding that the COVID-19 pandemic would make such an in-person summit more unlikely.
"I think it's probably unlikely between now and the USA election, as we see events being cancelled around the world", Biegun told a virtual seminar hosted by the German Marshall Fund's Brussels Forum on Monday.