Putin wants Kim to send Russia artillery shells and antitank missiles, while Kim would like Russia to provide North Korea with advanced technology for satellites and nuclear-powered submarines, the New York Times cited officials as saying.
The planned trip would come as Russia discusses holding joint military exercises with North Korea.
Russian Defense Minister Sergei Shoigu had reportedly tried to convince Pyongyang to sell artillery ammunition to Russia during a visit to North Korea.
The US has warned that North Korea could provide more weapons to Russia, whose forces invaded Ukraine in February 2022.
White House national security spokesperson John Kirby said last week that the US was concerned that arms negotiations between the two countries were advancing actively.
Kim exhibited North Korea’s banned ballisitc missiles to Mr Shoigu as the two countries pledged to boost ties in July.
Mr Shoigu arrived in North Korea along with Chinese delegates for the 70th anniversary of the end of the Korean War, celebrated in North Korea as Victory Day.
The missiles are banned under UN Security Council resolutions adopted with Russian and Chinese support, but were put on display for a show of solidarity between the three countries.
Mr Shoigu made the first visit by a Russian defence minister to North Korea since the fall of the Soviet Union.