The sources told Yonhap Kim's visit could start around 28 June and was likely to be to the Russian Far East because he travels by train rather than plane.
Russia shares a tiny border with North Korea. Kim visited the Russian province in August 2002.
He made a 24-day train journey through Russia on the Trans-Siberian Railway in July and August of 2001.
South Korean officials expressed doubt about Kim's reported trip, saying Russian Foreign Minister Sergey Lavrov was scheduled to visit North and South Korea in early July, Yonhap said.
"It's hard to believe that Kim would visit Russia just before the Russian foreign minister is expected to visit his country," Kim Young-Seok, head of the foreign ministry's European and Russian affairs bureau, was quoted as saying.
Meanwhile Japan's Kyodo news agency, citing a diplomatic source, said Kim planned to visit Russia for a summit with President Vladimir Putin in early July.
The summit may take place in the Pacific port city of Vladivostok, as did the last one between the two leaders in 2002, it said.
Putin visited Pyongyang in July 2000.
North Korea is known to have stepped up cooperation with Russia's Far East region in agriculture, forestry and energy.