Shadow treasurer Chris Bowen is running for the position of Labor leader, putting him in contest with colleague Anthony Albanese.
Mr Bowen, a member of the ALP right, will formally announce his bid on Tuesday morning in Sydney's Smithfield where he grew up.
Deputy leader Tanya Plibersek, from the left faction, ruled herself out on Monday, saying now was not her time.
Mr Albanese, also from the left, believes Labor needs to take a hard look at some of its policies after its shock federal election loss on Saturday.
"We got one in three Australians to vote for us. That's the truth. That is not good enough," he told 3AW radio.
He nominated the plans to dump cash rebates on franking credit for people who paid no tax, saying it was an issue many voters had contacted him about.
"In many cases people who were getting a relatively small amount ... but it was that two or three thousand dollars that they were using to pay their rates, to pay their car rego, for a holiday at the end of the year," he said.
"One of the options that could have been considered is putting a cap on it... You could have done a combination of that and grandfathering as well."
Nevertheless, he thought the Morrison government would have to act on the franking credits issue because its near $8 billion a year cost to the budget was unsustainable.
The leadership will be decided by a vote of grassroots members and the federal parliamentary caucus, with each group given 50 per cent weight.
Mr Albanese won the grassroots vote in 2013 but did not get enough caucus votes to defeat Bill Shorten.
Labor MP and finance spokesman Jim Chalmers, who also hails from the right, is now unlikely to run for the leadership despite saying on Monday he was considering it.
Joel Fitzgibbon is also considering a tilt, but only if the candidates don't promise to stand up for regional Australia and the coal-mining industry.
"I am considering doing so, yes, I would much rather someone else do it," the Hunter MP told Nine's Today program.
Mr Shorten will continue as Labor's interim leader until the party's leadership is determined.
Australian Associated Press