This suggestion comes off the back of South Korean President Moon Jae-in suggesting the counties could submit a joint bid for the 2030 World Cup.
Do will raise the idea of moving some of the skiing events north of the border when he meets the International Olympic Committee president, Thomas Bach, later this month, South Korean media said.
The proposal, which would amalgamate North and South Korea's women's hockey teams, is one of a number of efforts at rapprochement ahead of the February opening of the Games in the South Korean town of Pyeonchang. The Post quoted Jong-hwan as saying he hopes that North Korea will accept the olive branch and, in turn, make the 2018 PyeongChang Olympics a "peace Olympics".
Earlier this month, Moon proposed that the two countries put in a bid to Federation Internationale de Football Association to host the 2030 World Cup.
Do Jong-hwan, who was appointed minister of culture, sports and tourism last week, plans to discuss the plan with Chang Ung, North Korea's International Olympic Committee representative, at the World Taekwondo Championships in Muju in South Korea's North Jeolla Province.
The countries considered co-hosting the 1988 Summer Olympics, but those plans fell through and North Korea boycotted the games. 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.
North Korean athletes have made limited appearances at global sporting events like the World Cup and the Olympics, with two gold medals in Rio's 2016 games. The country may ask for a little help, too: from North Korea.
Do said he is also considering holding some of the Winter Games events in North Korea's new ski resort. USA officials arranged for his release last week, but Warmbier arrived home in OH in a coma-like state with severe brain damage.
However, the pivot towards reconciliation with North Korea could raise eyebrows in the U.S., where President Donald Trump's early days in office have been marked by heightened tension with the communist state.