There has been speculation in both North Korea and the United States that Trump may be feigning unpredictability, emulating former USA president Richard Nixon's "Madman Theory" -whereby enemy countries were tricked into avoiding conflict with the U.S., believing Nixon would be irrational and unpredictable in his response.
Song would be the first ministerial-level Chinese official to visit North Korea since October 2015.
Throughout the Asian trip, Donald Trump made a significant attempt to unite the Asian governments in an attempt to curb down North Korea's nuclear global threat, in addition to making offensive, insulting remarks against Kim Jong Un, the current leader of North Korea.
The state-run media outlet criticized Trump for slandering "the happy life of the great Korean people" by presenting real, well-documented examples of North Korean atrocities against its own people, such as the brutal prison camps where hundreds of thousands of people experience unimaginable horrors and the theft of state resources by elites as the people starve.
Song's visit, however, will more likely be about small steps than big successes. "Progress is being made", the president tweeted.
They hoped the North could freeze its nuclear missile programmes in exchange for the US and South Korea halting the military drills Kim considers as preparation for invasion. Its uncompromising line has helped put its former close alliance with its neighbor China into a deep chill.
Robert Kelly, associate professor in political science at Pusan National University in South Korea, told the LA Times: "The optimistic spin is that Donald Trump got through to the Chinese, and maybe the Chinese are taking this seriously - they're going to send somebody to Pyongyang to talk about coming around on the nuclear programme".
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Shortly following his visit, Japan announced additional sanctions on 35 North Korean entities and individuals.
Following last week's meetings - which were part of Trump's five-nation Asia tour - the president sounded optimistic in a Twitter message.
China is the linchpin of any such effort, and in Beijing Trump said it can fix the North Korea problem "easily and quickly".
Trump added that it would be "very, very nice" to have a good relationship with Kim.