Australian representation on the U.N. panel is out of reach for now because of former Prime Minister John Howard's decision not to take a seat four years ago, and due to agreements with other countries, The Sydney Morning Herald reported Sunday.
Current Prime Minister Kevin Rudd's government is exploring a bid for one of the council's 10 non-permanent positions, however.
Australia, which is a founding member of the council, has sat on the body four times, the last time in 1985-86. It last tried to join the panel in 1996 but failed, the newspaper reported.
Former Foreign Minister Alexander Downer told the newspaper it would have cost $35 million to lobby for another two-year term beginning in 2008.
"I was very keen to run," Downer said. "It was always my view that Australia was a significant country that should, from time to time, be on the Security Council."