When Rodman visited the North in February 2013 with the Harlem Globetrotters, an exhibition basketball team, Kim was said to have personally gifted him with a present that said, "For our friendship".
The former National Basketball Association player is travelling as a private citizen.
"But one thing we know is that Trump is transactional", one official told the newspaper.
Rodman appeared Trump's "The Apprentice" show, and the pair have had an up-and-down relationship.
"My goal is to go over there and try to see if I can keep bringing sports to North Korea", the athlete told reporters at the airport.
As he left for the isolated autocracy from Beijing on Tuesday, Rodman told reporters that he believes Donald Trump would support the visit as a means to "accomplish something we both need".
The last time Rodman visited the country was in January 2014, when he and a group of former basketball players participated in an global basketball exhibition which was marked as a birthday gift for Kim Jong Un, who is a big time basketball fan.
The US state department said it is aware of his visit.
North Korea has released Cincinnati native Otto Warmbier, a 22-year-old college student who had been detained and imprisoned in that reclusive dictatorship for more than a year.
North Korea has released college student Otto Warmbier, and the American is on his way back to the US, says Secretary of State Tillerson.
Another US Appeals Court Rules Against Trump's Revised Travel Ban
The American Society of Travel Agents (ASTA ) has said that it is waiting to see how the policy will impact U.S.travel agents. It cited the president's campaign statements calling for a "total and complete shutdown" on Muslims entering the U.S.
Marijuana is heavily controlled and illegal for citizens of North Korea to buy and consume.
Rodman endorsed Trump for president in July of 2015, not long after his candidacy was announced in Trump's infamous "Mexicans are rapists" speech. Rodman also publicly told Kim that he "had a friend for life" in front of hundreds of North Korean spectators.
The basketball Hall of Famer has faced ridicule and criticism for his trips to North Korea, which some USA politicians and activists view as serving only as fodder for North Korean propaganda.
Rodman was filmed leading a sing-along of "Happy Birthday" to the North Korean leader, a man he calls a friend and a "very good guy", but is widely seen as a brutal dictator who once lauded the execution of his own uncle.
In 2014, he told luxury lifestyle magazine DuJour he had approached the United States government for support but was rejected.
Do you ever have any question about anything you wish to ask and get answer?
He has previously broken down in tears during TV interviews, saying he has had death threats over his trips, which have been condemned by human rights activists.
A foreign ministry official who spoke to the AP in Pyongyang confirmed Rodman was expected to arrive Tuesday but could not provide details.
Mr Bae later thanked Mr Rodman for raising public awareness of his case.
Worldwide diplomacy between the United States and North Korea has been handed over to Dennis Rodman and sponsored by a cryptocurrency for weed, because 2017 is weird as hell. He wore fully branded clothes to the airport. Volo has accompanied Rodman on previous trips to the dictatorship.
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