Seoul's new president -- who backs engagement with the nuclear-armed North -- made the suggestion at the World Taekwondo Federation championships in Muju last weekend.
In South Korea's Pyeongchang next year, Moon said he would like to see again "the glory" of past events "where the South and the North achieved the best-ever results by fielding joint teams".
He also suggested the two Koreas jointly participate in the Games' opening ceremony, as they did at the 2000 Summer Olympics in Sydney.
But no North Korean athletes have so far qualified for Pyeongchang, raising the prospect that none will attend in any case.
In Muju, Bach said he appreciated "the message of President Moon to see the Olympic Games as a possibility for dialogue and reconciliation".
He would discuss "what could be done in this respect" in talks with Moon on Monday, after the South Korean leader returned from a visit to the United States, he added.
Tensions are high on the Korean peninsula over the North's nuclear and missile development.
But at the World Taekwondo Championships a delegation from the rival North Korean-led, Austrian-based International Taekwondo Federation performed a demonstration, and World Taekwondo chief Choue Chung-won said Friday they had agreed a WT group would reciprocate at the ITF championships in Pyongyang, the North Korean capital, in September.
The last chance for North Koreans to qualify on merit is September's Nebelhorn Trophy figure skating in Oberstdorf, Germany, where two pairs skaters will seek to do so.
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