Opinion polls in Australian newspapers on Saturday show former Labor leader Kevin Rudd is more popular with voters than current prime minister Julia Gillard.
But the ABC reports readers are more equally divided over whether Labour should change leaders.
Mr Rudd was deposed by Ms Gillard in June 2010.
The latest Newspoll favours Mr Rudd, with 53% of those polled saying he is the preferred Labor leader, compared with 30% supporting Ms Gillard.
The poll also found that 48% say Mr Rudd is preferred prime minister to Tony Abbott, on 40%.
Supporters say the caucus must take heed of his popularity as shown in the opinion polls.
Labor caucus members are to vote on Monday to decide who should lead the party. Labor has 103 members.
Mr Rudd has told voters that Labor would lose the next election under Ms Gillard.
He said he was acting to save Australia from the "ravages" of a Coalition government led by Mr Abbott.
