The announcement came after the rogue regime’s Olympics delegate Gen Kim Yong-chol met South Korean President Moon Jae-in before the closing ceremony of the Winter Olympics in Pyeongchang.
Mr Trump's daughter Ivanka attended the ceremony on Sunday alongside the North’s delegate Kim Yong-chol.
Kim Yong-chol said the North Korean leader wanted to improve ties with Washington and had "ample intentions of holding talks", according to the South's presidential office.
The possibility of talks comes after Mr Trump and Kim Jong Un became embroiled in a public war of words over the North’s series of ballistic missile tests and nuclear programme.
Mr Trump said earlier this week that the US was imposing the “largest ever” set of sanctions on North Korea, including measures to target more than 50 of its ships and maritime companies.
The rogue state is already under a range of international and US sanctions, but it last year it continued to test weapons.
It also tested a nuclear weapon and long-range ballistic missile capable of hitting the US.
Today's announcement also came as US officials said the North had pulled out of a meeting with Vice President Mike Pence during the opening ceremony of the games.