Tony Abbott, a former health minister, and Malcolm Turnbull, the former environmental minister and a former Goldman Sachs Group executive, are running for the post, The Financial Times reported Monday.
Also in the race is former foreign minister Alexander Downer, former education minister Julie Bishop and former defense minister Brendan Nelson.
Peter Costello, the country's former treasurer and anointed by outgoing Prime Minister Ron Howard to succeed him as party leader, announced he would not run for the job.
The Liberal Party lost 26 seats in Saturday's election, the party's worst defeat since it was founded in 1944. The Labor Party now holds government in all states and at the federal level.
Michael McKinley, a political scientist at the Australian National University, told the Times the size of the Labor Party's majority does not mean the party will be able to maintain its political dominance for several terms.
"Because this is a new government, any sudden shift in the economy will reverberate," McKinley said. "Labor is walking on eggshells."