Kono, who has previously met with Kang to discuss cooperation, is expected on Wednesday to request unabated pressure on Pyongyang and even assistance on the issue of abducted Japanese citizens, South Korean news service Newsis reported.
But the focus will stay on North Korea denuclearization and the objective of complete, verifiable and irreversible dismantlement, or CVID, of Pyongyang's weapons of mass destruction, according to the report.
While Seoul and Tokyo are aligned on the issue of North Korea denuclearization, the two countries have often been at odds over historical issues, including policies addressing the issue of wartime "comfort women" enslaved in Japanese brothels during World War II.
Important issues may be at stake for Japan, however.
Yonhap reported Kono might also deliver a deeply significant diplomatic gesture with a visit to the Seoul National Cemetery, reserved for deceased veterans of the Korean War, the Vietnam War and fighters for Korean independence.
South Korean foreign ministry spokesman Noh Kyu-duk said there is a precedent for a potential Kono visit to the cemetery.
A Japanese diplomat visited the cemetery in 2004, Noh said.
A cemetery visit could improve ties between the two countries.
In March 2015, former Foreign Minister Fumio Kishida canceled plans to pay tribute to South Korea's war dead, as bilateral relations declined between the two countries.
South Korean President Moon Jae-in is expected to hold a summit with Kim Jong Un on April 27.