In a rare trip abroad, Kim would travel from Pyongyang, probably by armoured train, to Vladivostok, on the Pacific Coast of Russia, where he would meet Putin, the New York Times reported on Monday, citing US and allied sources.
While in Vladivostok, a port city not far from North Korea, the two leaders would discuss Kim's sending Russia artillery shells and antitank missiles in exchange for Moscow's advanced technology for satellites and nuclear-powered submarines, the newspaper reported.
At a time when the United States has expressed concern about growing military ties between the two countries, the news of Kim's planned visit came after Russia said it was discussing holding joint military exercises with North Korea.
"Why not, these are our neighbours. There's an old Russian saying: you don't choose your neighbours and it's better to live with your neighbours in peace and harmony," Interfax news agency quoted Russia's Defence Minister, Sergei Shoigu, as saying on Monday.
When asked about the possibility of joint exercises between the two countries, he said they were "of course" being discussed, it said.
South Korean news agency Yonhap earlier cited South Korea's intelligence agency as saying Shoigu, who visited Pyongyang in July, had proposed to Kim that their countries hold a naval exercise, along with China.
The Kremlin said last week that Moscow intends to deepen its "mutually respectful relations" with Pyongyang, one of its close Cold War allies and also one of a small handful of countries to back Russia's proclaimed annexation of parts of Ukraine in 2022.
The New York Times reported Kim could possibly go to Moscow, although that was not certain.
Kim's father, the reclusive Kim Jong-il who famously shunned planes and travelled by armoured train only, last visited Russia months before his death in 2011.
Shoigu visited North Korea for the 70th anniversary of the end of the Korean War in July, celebrated in North Korea as Victory Day, with South Korea's National Intelligence Service saying that he appeared to have held a private meeting with Kim, Yonhap reported.
The US last week said it was concerned that arms negotiations between Russia and North Korea were advancing actively, and that Shoigu had tried during his visit to convince Pyongyang to sell artillery ammunition to Russia.
On Saturday, Russia's ambassador to North Korea, Alexander Matsegora, told TASS news agency that he was not aware of any plans for North Korea to participate in trilateral military drills with China and Russia, but that in his opinion it would be "appropriate" in light of US-led exercises in the region.
Russia and North Korea have recently called for closer military ties but North Korea has denied having any "arms dealings" with Russia.
The US recently imposed sanctions on three entities it accused of being tied to arms deals between North Korea and Russia.
North Korea has conducted six nuclear tests since 2006 and had been testing various missiles over recent years but it rarely holds military exercises with its neighbours.
The US and its ally, South Korea, hold regular military exercises, which North Korea denounce as preparations for war against it.Â
