Fischer, who has been in detention since July 13 when he was stopped from leaving Japan at Tokyo's main international airport, said he would accept deportation if Japanese authorities refused to simply let him leave, the BBC reported.
Iceland offered last week to accept Fischer.
U.S. officials are seeking the chess genius for allegedly violating international sanctions against Yugoslavia in 1992. Fischer held the title of world chess champion until 1975 and resurfaced in Yugoslavia for a dramatic 1992 rematch against former champion Boris Spassky, whom he beat in a match hosted by Iceland.
Fischer then disappeared when U.S. authorities announced they wanted to prosecute him over the $3 million he earned for playing the game, which Washington said violated U.S. and U.N. bans on doing business in the country.
Fischer could face 10 years in jail if prosecuted in the United States.