"Hopefully we'll be able to ease lingering tensions as we try to bring North Korea on board", Do said, adding that he was also considering carrying the Olympic torch in North Korean cities such as Kaesong or Pyongyang.
Such a collaboration could help the neighbors resume dialogue after a period of official silence.
What Pyongyang thinks of the proposals is not yet clear.
North Korea's only member of the International Olympic Committee (IOC), Chang Ung, said on Friday that he will discuss a plan to form a unified Korean team during the Pyeongchang Olympics with other IOC members.
The sports minister further said that both Nation could co-host the ski resort even with Jang Woong, who is the delegate of North Korea to the IOC.
The Games are to be held in PyeongChang, which is just 40 miles from the demilitarized zone separating North from South.
Huge, homely mastiff named Martha wins world's ugliest dog
The 3-year-old hound beat out 13 other canines for the title, including a bald Chinese Crested pooch and a mixed breed named Icky. The victor of the 29th annual contest held at Sonoma-Marin Fair will be decided Friday evening.
"If the neighboring countries in northeast Asia, including North and South Korea, can host the World Cup together, it would help to create peace", Moon said.
No North Korean athletes have qualified for the 2018 games.
In a commentary Friday, North Korean state-controlled newspaper Rodong Sinmun said that if South Korea pursues peace with the North, it should "stop all hostilities", including sanctions.
Tension has been high for months over North Korea's nuclear and missile development, and due to fears it will conduct a sixth nuclear test and more ballistic missile launches in defiance of U.N. Security Council resolutions.
The NHL failed to come to an agreement with the International Olympic Committee on sharing the revenue generated by hockey at the Olympics, as well as on the insurance for the league's players.
North Korean officials have reportedly declared the country's intent to take part in the Olympics after they boycotted the 1988 Summer Games in South Korea's capital Seoul.
Taeyang joins a list of ambassadors from the worlds of sport and entertainment to promote the Games that run from February 9-25.