The suggestion was presented to FIFA President Gianni Infantino as he visited Seoul to attend the FIFA Under-20 final match.
"If East Asian countries, including the two Koreas, host the World Cup, I think this will help ease tensions on the Korean Peninsula as well as the entire region. I hope this can happen with the 2030 FIFA World Cup," Moon said.
Infantino said that he would offer the idea to Chinese President Xi Jinping when he visits China later this week. He added there would be "difficulties" in arranging a co-hosting of the World Cup by a consortium of countries to include North Korea, but admitted the message of peace "can be a very powerful message."
There was no immediate response from North Korea.
South Korea and Japan co-hosted the 2002 World Cup, and several countries and groups of countries are bidding to host the 2030 tournament.