The Weekend Australian newspaper said a Malaysian, Azman Hashim, spent nearly a year in Sydney conducting the training exercises in the Blue Mountains west of the city.
About three dozen men, all accused of being members of the Al Qaeda (search)-linked group, have been arrested for the Bali (search) bombings in Indonesia in October that killed 202 people, most of them foreign tourists.
Police told the Australian newspaper there was "nothing to suggest" Hashim's time in Australia posed any threat to the Olympics.
"However, they have confirmed that his presence here stemmed from a concerted effort to transform the Australian JI cell, known as Mantiqi 4, into a group with the training and capabilities of its three sister cells in Southeast Asia," the newspaper said.
On his return home in 2001, Hashim was detained by the Malaysian Special Branch -- a police unit with wide-ranging powers which has detained and interrogated religious extremists and opposition politicians -- and remains imprisoned.