It comes after Kim Jong-un said in his New Year speech that he is considering sending a team to Pyeongchang in South Korea for the Games and that the two sides should “urgently meet to discuss the possibility”.
South Korean Unification Minister Cho Myoung-gyon said the South proposes the two countries meet on January 9 at the border village of Panmunjom to discuss the games and also to improve overall ties.
President Moon Jae-in said he had already proposed making the games a ” groundbreaking chance” to move towards peace.
He added the relevant ministries should “swiftly come up with follow-up measures to quickly restore South-North Korean dialogue”.
But he said pressure to stop North Korea’s controversial nuclear and ballistic weapon development would continue.
In his speech, Kim Jong-un repeated threats against the US and said the country is now within the range of North Korean weapons and the nuclear button is “always on my table”.
In an unusually softer tone, he also said the frozen relationship should “melt”.
He said: “The year 2018 is a significant year for both the North and the South, with the North marking the 70th anniversary of its birth and the South hosting the Winter Olympics.
“We should melt the frozen North-South relations, thus adorning this meaningful year as a year to be specially recorded in the history of the nation.”
President of the Pyeongchang Games’ organising committee, Lee Hee-beom said he was delighted to hear of the potential participation.
He added: “It’s like a New Year’s gift.”
The only North Korean athletes who have qualified for the game are figure skaters Ryom Tae-Ok and Kim Ju-Sik.
North Korea has missed the official deadline to confirm their participation in the games, but they can still compete with an invitation by the International Olympic Committee.
But analysts say Kim may be trying to drive a wedge between Seoul and its ally Washington as a way to ease international isolation and sanctions against North Korea.
Douglas Paal, a former senior US diplomat, said: “This speech pokes at the fissure that has lain below the surface in U.S.-South Korean relations, and seems designed to drive a wedge there.
“President Moon needs a successful Olympics and the US drive to increase pressure fits poorly with the Southern agenda.”
Evans Revere, another former senior US diplomat who took part in unofficial talks with North Korean officials last year, said Pyongyang would likely try to extract concessions as a “price” for Olympics participation.
However, he added: “It’s hard to imagine Seoul falling for this.”
South Korea and the US have so far remained allied in their pressure and isolation campaign of North Korea despite repeated calls from Kim Jong-un for Seoul to sever its with Washington in a bid for “peace”.
Responding to Kim Jong-un’s offer a spokesman for the South Korean presidency said: “We have always stated our willingness to talk with North Korea anytime and anywhere if that would help restore inter-Korean relations and lead to peace on the Korean Peninsula.”