Mr Trump said in Beijing last week that the world must "act fast" to confront Pyongyang's development of nuclear weapons.
Chinese President Xi Jinping will send his special envoy to North Korea this week, the countries' state media reported Wednesday, amid strained ties over Pyongyang's nuclear program.
The announcement did not mention Trump or the U.S. However, it's believed that China's new nuclear point man also has not yet visited North Korea in this role.
The UN sanctions include China closing all North Korean businesses and joint ventures in China, capping oil supply and preventing any more North Koreans from working in China to earn cash for the regime.
The announcement came a day after the end of Trump's five-nation tour of Asia, during which the United States leader held meetings with Xi and urged him to act fast to rein in North Korea, warning that "time is quickly running out".
Following last week's meetings - which were part of Trump's five-nation Asia tour - the president sounded optimistic in a Twitter message.
USA officials want Chinese authorities to clamp down on unauthorised trade that they say is still trickling across the North Korean border.
Song would be the first ministerial-level Chinese official to visit North Korea since October 2015 when Politburo Standing Committee member Liu Yunshan visited Pyongyang and met with Kim.
Song, the head of the International Department of the Communist Party of China (CPC), is expected to convey the outcome of Xi-Trump talks and Washington's emphasis on Pyongyang giving up the nuclear and missile programme for resumption of dialogue and lifting of sanctions.