Fischer, 61, has been in custody for two weeks after being detained by Japanese immigration officials when he attempted to fly out of Japan with a U.S. passport that had been revoked.
He is being held at Tokyo's Narita airport since July 13 for violating Japanese immigration law after trying to leave for the Philippines, Voice of America reported.
Japanese immigration authorities turned down his appeal against deportation, although he had until Friday to appeal to the Japanese justice minister.
The United States revoked his passport for violating economic sanctions against the former Yugoslavia in 1992 when he played a chess match there in 1992 against rival Boris Spassky.
Meanwhile, Japanese politician and ardent chess player, Ichiji Ishii, says he is willing to act as Fischer's legal guarantor, if that will secure his provisional release.
Other supporters say they are trying to help secure a German passport for Fischer, based on the fact that his late father was a German citizen.