Preliminary polling results in six seats in the state of Victoria show a collapse in Labor's primary vote to 35%.
The Australian reports Labor faces two-party-preferred swings of up to eight per cent in inner Melbourne and 15 per cent in outer-suburban seats.
AAP reports Labor MPs are reeling from a string of devastating polls predicting electoral ruin, with speculation rife that Ms Gillard's key backer is under mounting pressure to call on the prime minister to resign.
And the ABC understands Prime Minister Julia Gillard has lost significant support in the Labor caucus.
ABC Insiders presenter Barrie Cassidy said former prime minister Kevin Rudd is the only figure being considered as an alternative prime minister.
Mr Cassidy spoke about the tensions within the party on Insiders on Sunday.
"I am now very strongly of the view that Julia Gillard will not lead Labor into the next election," he said.
"I think there will be a change either by her own hand or the actions of others. And I'm not relying entirely on guesswork here."
Writing for ABC's The Drum, Mr Cassidy said key Labor players are now planning when and how Ms Gillard should be approached to step aside.
"Those who have changed their thinking are convinced that in any case, she must be close to deciding for herself that continuing on through a torrid and hopeless 10-week campaign is intolerable," he wrote.
Polling last Monday showed the party could be left with as few as 40 seats in the federal parliament after the election on 14 September.
The ABC reports two long-serving MPs have already packed up their Canberra offices in preparation for the electoral wipe-out.