Fischer currently is being held in Tokyo and is wanted in the United States for violating international sanctions against Yugoslavfia in 1992.
He has no valid passport and is awaiting a German decision on whether to grant him one on the grounds he had a German father.
Fischer's 1972 match against Russian Boris Spassky took place in Iceland. In an interview to Icelandic television earlier this week, he said, "I hope the Icelandic government grants me political asylum."
Fischer also is applying for asylum in Japan, the BBC said.
A brilliant but mercurial player, Fischer became a grandmaster at 15 and shot to fame in 1972 when he beat Boris Spassky of the then Soviet Union. He held the title of world chess champion until 1975, fell from the public eye and then resurfaced in Yugoslavia for the dramatic 1992 rematch against Spassky.