From Laurie Oakes.
Nine's political editor Laurie Oakes reported on Tuesday that Rudd backers had raised the prospect of a leadership move with caucus colleagues.
The move could come within days, possibly Friday, it was reported.
Parliament rises on Thursday and won't sit again until the federal budget on May 14.
Meanwhile, senior Labor figures have pledged their support for Prime Minister Julia Gillard, despite internal criticism of the federal government's handling of two major policies.
The Labor caucus met for two hours on Tuesday for the last time before the May 14 budget.
While sources said the leadership issue wasn't raised, a number of MPs were critical of the prime minister's handling of changes to single-parent payments and media law changes.
Adding to tension was a Fairfax Media report saying two ministers, Bob Carr and Mark Butler, had withdrawn their support for Ms Gillard.
While Fairfax stood by its story, Senator Carr, who is in Washington, DC, denied it.
"The prime minister has my unqualified support," Senator Carr said.
"I think the media's in a frenzy of speculation."
Mr Butler used Twitter to clarify his position: "Still a proud member of Julia Gillard's team, contrary to latest media frenzy."
Former leader and senior minister Simon Crean also said the prime minister had his full support.
"There's never been a more loyal person in terms of the leadership of the Labor Party," he told reporters in Canberra.
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