Chairman Paul Stapleton has spoken about the talks and the hope that they will be concluded by mid June.
The discussions will take place with George Synan, the director of Kagami's Shonan Management Corporation.
"We've got to do what's best for the football club. That's why we're taking our time. We have to make sure the club is protected," Stapleton said.
"My personal opinion is that if anything is concluded, it won't be concluded before the board meeting on 15 June," he added.
Kagami has been a director of the Pilgrims since April last year.