According to DiMaggio, North Korean officials have also been questioning Trump's "mounting problems" in the USA, not least "the investigation being conducted by Robert Mueller" over the president's ties with Russian Federation.
On Saturday, Kim's government responded by accusing Trump of trying to demonize North Korea, keep it apart from the worldwide community and undermine its government.
"They really want to know what is his end game", said DiMaggio, a scholar at New America who specializes in talking with rogue regimes and has spent almost two decades in secret discussions with the North Koreans.
US President Donald Trump has praised his own ability as an arbitrator, offering to mediate in the South China Sea dispute.
Trump has been working to rally global pressure against North Korea's nuclear weapons program on a trip to Asia.
North Korea is not known to have tested any of its missiles or nuclear devices since September 15, a relative lull after a brisk series of tests earlier this year.
North Korea said Trump is a "destroyer" who "begged for nuclear war" during the president's tour of Asia.
That makes sense, but when world leaders such as former businessman Donald Trump and dictator Kim Jong-un are throwing school yard insults at each other, it's hard not to stick your nose in.
The two leaders are schoolyard barbs amid heightened tension between North Korea and the United States.
Trump is now in Vietnam attending the Asia-Pacific Economic Cooperation summit, but he took the time to tweet: "Why would Kim Jong-un insult me by calling me 'old, ' when I would NEVER call him 'short and fat?'".
The Washington Post reported in September that North Korean officials had been trying to set up meetings with Republican-tied analysts in Washington to try getting a better understanding of Trump and his mixed messages.