North Korean leader Kim Jong Un is not expected to visit the South before the end of the year, South Korean President Moon Jae-in’s office said Wednesday.

Kim may still travel to Seoul in January for what could mark the first trip by any North Korean leader to the South’s capital, presidential spokesman Yoon Young-chan said in a text message. Yonhap News reported earlier that South Korea ruled out any visit by the North Korean leader to Seoul this month.

For several weeks, South Korea has been abuzz with rumors and speculation about Kim’s possible trip to the South, with groups for and against him holding rallies on the streets of Seoul.

In September, South Korea’s president met Kim in Pyongyang and agreed to host him in Seoul before year’s end, a move resisted by other North Korean leaders due to security concerns.

The two Koreas have taken a number of steps to improve their ties and resume inter-Korean exchanges, including holding three summits, in a dramatic shift from last year when North Korea’s nuclear and missile tests brought the Korean Peninsula to the brink of conflict.

Nuclear negotiations between the U.S. and North Korea have stalled in recent weeks as North Korea canceled a high-level meeting with American officials at the last minute and doubts have been raised about a second summit between Kim and U.S. President Donald Trump.