Senior Labor figures are lobbying former treasurer Wayne Swan to throw his hat into the ring to become ALP president, in a move that could blow the race wide open and create a potential headache for Opposition Leader Bill Shorten.

The position is held by shadow cabinet member Mark Butler, who delivered a scathing attack on the party's factional warlords last week. It's understood he now plans to run for a second-term unless another strong pro-reform candidate emerges ahead of the ALP National Conference in July.

Mr Butler's decision to highlight Labor's consistently low primary vote - and contrast it unfavourably with that of former leaders Kim Beazley, Mark Latham and Kevin Rudd, who all polled in the 40s - has also been interpreted as thinly veiled swipe at Mr Shorten, and has infuriated supporters of the opposition leader.

Transport Workers Union secretary Tony Sheldon is already in the mix as a candidate for the Right faction; however, Mr Swan is also being discussed as an alternative candidate as the Right weighs how to seize the influential role from the Left, which typically holds the post.