Jong Un, his younger brother from another mother, was named the new leader after their father died in late 2011.
Police have described the incident as a "sudden death", pending the results of a postmortem investigation.
The Royal Malaysia Police said in a statement that a North Korean man they identified as Kim Chol - an alias that South Korean officials said had been used by Kim Jong Nam - died en route to a hospital on Monday after seeking medical assistance at the airport. South Korea also reportedly jailed a North Korean spy in 2012 who admitted to trying to organize a hit-and-run accident targeting Kim Jong Nam in China in 2010.
Outside analysts had once assumed that Kim Jong-nam, the eldest son of former leader Kim Jong-il, could be the intended heir after his father, whose own father, Kim Il-sung, founded the Democratic People's Republic of Korea after World War II.
He said he wanted to visit Disneyland.
The older brother was believed to be close to his uncle, Jang Song Thaek, who was North Korea's second most powerful man before being executed on Kim Jong Un's orders in 2013.
With Kim Jong Nam out of the picture, you might assume that Kim Jong Chul, the middle son, would be the natural choice for a new heir. "He's too young and he didn't have enough time to be groomed". Last year, Kuala Lumpur hosted secret talks between top North Korean officials and former USA diplomats, the only remaining communication channel between the two sides. Up until about 2012, Kim Jong Nam was said to be, a Chinese administrative region the Week once compared to Las Vegas. Kim Jong Nam's son, now 21, once posted photographs of himself wearing a cross and has spoken out about humanitarian issues such as human rights and starvation in North Korea.
Following his father's death in December the following year, Kim's comments about his younger brother's ability to maintain "absolute power" to a Japanese journalist singled him out as his most vocal, and high profile, critic.
Speculation quickly spread in South Korea on Tuesday that Kim Jong Un might be behind the reported death of his half brother. He said that Kim died on his way to the hospital.
Mr Kim was waiting at the airport's Terminal 2 to board a flight to Macau, according to Malaysian police.
"We don't know if there was a cloth or needles; the receptionist said someone grabbed his face, he felt dizzy, " the official said. A book about the Kim family called Under the Loving Care of the Fatherly Leader reported that he became "a familiar figure" at a bathhouse in Yoshiwara which is one of Tokyo's red light districts in the late 1990s. "He (Kim Jong Nam) sees his brother failing".
Fadzil said an ambulance picked up Jong-Nam from the airport.
Kim Jong Nam had arrived in Malaysia on February 6 and was attacked Monday before boarding a plane to Macau, according to the Malaysiakini online news outlet.
Kim Jong Il had at least three sons with two women, as well as a daughter by a third. He had been very critical of the regime. He doubted how those who support his father or his successor really care for the well-being of ordinary North Koreans. He's also older than Jong-un, and perhaps a potential rival if factions develop in Pyongyang seeking to depose Jong-un.