At a major summit, the two leaders gave no details of which cities might host certain events at the games, or how advanced the plans were.
The International Olympic Committee traditionally does not announce host cities until seven years ahead of the games. That would give the Koreas until 2025 to put together a joint bid.
Germany has already announced plans for a multi-city bid for 2032, as has Brisbane, Australia. The India Olympic Committee has also indicated its interest in hosting the 2032 Games.
A successful bid by the Koreas would mark the second time South Korea hosted or co-hosted the Summer Games, the first being 1988 in Seoul. South Korea also hosted the Pyeongchang Winter Games in February.
Asia also features in the next two Olympics — the 2020 Summer Games in Tokyo and the 2022 Winter Games in Beijing, which also hosted the summer version in 2008.