The reports come after the surprise announcement that US President Donald Trump plans his own talks with the North Korean leader, part of fast-paced diplomatic developments following an Olympic detente.
However, there have been no public proposals of talks by either Pyongyang or Tokyo.
Japan's Kyodo news agency reported a potential Abe-Kim summit today, citing unnamed government sources who said the talks could be part of a new approach by Tokyo to dealing with the North.
Hours later, Jiji Press reported a similar story, saying Tokyo fears being left behind in dealing with the North if talks proceed between the isolated nation and South Korea and Washington without Japan's involvement.
Contacted by AFP, a foreign ministry spokeswoman said she could not confirm any concrete plans for a summit.
But she added "we will be studying our policies from the viewpoint of what is most effective" to resolve the issues of North Korea's nuclear and missile programmes as well as the abduction of Japanese citizens by Pyongyang.
Earlier this week, South Korean envoy Suh Hoon visited Tokyo to brief Japan's leadership on the fast-moving diplomatic process that saw an announcement last week of a historic US-North Korea summit to discuss Pyongyang's denuclearisation.
Suh, the chief of South Korea's National Intelligence Service, yesterday met with Abe but it was unclear if he brought a message from the North Korean leader to propose a summit with Japan.
Media reports and experts say Tokyo fears it may be left out of developments around North Korea, and worries that the issue of abducted Japanese citizens is being sidelined.
But the possibility of an Abe-Kim summit also comes as the Japanese premier faces a growing scandal at home over the sale of government land to one of his supporters, and an apparent cover-up of the deal by the finance ministry.
Abe rose to political prominence on his calls for a tough line on North Korea, particularly over its abductions of Japanese citizens.
Japan, a close US ally in the region, is in the firing line of North Korean missiles and saw two fly over its territory in 2017, sparking outrage and lifting tensions to fever pitch.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)