The announcement, made by sports minister Do Jong-hwan, is the latest in a series of olive branches waved by Seoul's new administration created to thaw relations with Kim Jong-un's regime north of the border.
He also said he can relay Seoul's wish for the creation of a unified team to the North Korean government, indicating that he may play a bridge role between the governments of the two Koreas concerning the issue.
What Pyongyang thinks of the proposals is not yet clear.
Do said he wants to meet with IOC President Thomas Bach and North Korea's IOC representative Chang Ung at the World Taekwondo Championships in Muju, North Joella Province late this month. According to a report by The Guardian, South Korea is attempting to see if North Korea can host some events to help improve peace relations.
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Also being considered are whether a unified female ice hockey team could be formed between the two Koreas or if North Korea's cheerleading squad could attend the winter games, set to be held February 9-25 in South Korea's northeastern region, the daily reported.
Do said he hoped North Korea's participation in the Winter Olympics would make Pyeongchang a "peace Olympics".
Speaking to reporters Friday, Chang said he was "aware that much has been discussed in the media" about a potential co-hosting agreement, and said he would pass on what he was told to Pyongyang.
"We are more than willing to talk about the ideas that he is proposing because the Olympic is always willing to build bridges and bringing down walls".
A liberal candidate from the Democratic Party, Moon has pledged greater dialogue with North Korea in a bid to reduce tensions. However, the country is not known for competing well in Winter Games and was notably absent for the 2014 Olympic Winter Games held in Sochi, Russia.