Kim used a very distinctive armored train made especially for him on visits to China previous year.
In his New Year's speech, the North Korean leader said he was ready to meet with Trump at any time to produce an outcome welcomed by the global community.
Trump's comments Sunday seem to be a call for North Korea to return to a fresh round of high-level talks, said Shin Bum-cheol, a senior fellow at the Seoul-based Asan Institute for Policy Studies.
In an interaction with reporters at the White House, Trump said he had had "indirect" talks with Kim.
In the Chinese border city of Dandong, dozens of security vehicles and officials blocked the roads around the train station on Monday before the train passed through, Yonhap reported, before reopening them afterwards.
The train crossed the border around 10.15 pm local time (9.15pm Singapore time) and was expected in the Chinese capital Tuesday (Jan 8) morning, the South Korean news agency reported, citing an informed source.
Kim started off his flurry of summits a year ago with a meeting with Xi.
None of Kim's 2018 trips to China were announced in advance, and the earliest indications of the first one - before Kim met either Moon or Trump - came when his train was spotted in Beijing. Korean language watermark on image as provided by source reads: "KCNA" which is the abbreviation for Korean Central News Agency.
But progress has stalled since the Singapore summit with the two sides disagreeing over the meaning of their vaguely-worded declaration, and the pace of US-North Korean negotiations has slowed, with meetings and visits cancelled at short notice.
Diplomatic sources say Xi will probably go to North Korea at some point soon, which would make him the first Chinese leader to do so since 2005. Trump said his administration has a "very good dialogue" with Pyongyang, adding: "Now I say this, North Korea, we're doing very well".