Mizumoto, 22, has reportedly been frustrated that he has not been given enough playing time ahead of the Olympics. The Nikkan Sports daily said Friday he would likely go to fellow first division side Kyoto Sanga.
The defender moved to Gamba Osaka this year under a three-year contract, but he has started only twice since the season opened in March.
"The club has consistently tried to persuade him to stay but in the end decided to respect his wishes," Gamba Osaka said on its website.
Gamba Osaka is expected to ask the next club to pay a transfer fee, estimated to be about 300 million yen (2.78 million dollars), along with a penalty for Mizumoto breaking his contract.
Mizumoto was discovered by former Japan coach Ivica Osim when playing for JEF United Ichihara - now JEF United Chiba - as the Bosnian raised the J.League outsiders into title contention.