Rudd, now foreign minister, was ousted in a shock party coup in June 2010 by his deputy Julia Gillard. She is now badly lagging in the polls and talk has intensified that he is preparing to challenge for the top job.
Party insiders were cited by the media as saying a leadership ballot could come as early as next Monday, when parliament sits again.
Rudd is currently in Mexico for the G20 meeting.
Former Labor leader Simon Crean launched a scathing attack on the foreign minister Monday, saying he had been "internally disloyal".
He said Rudd needed to be a "team player" and that he should "put up or shut up" to resolve the long-running speculation.
"If Kevin Rudd can't be part of the team, let him exit the team," he told ABC radio. "If he thinks he's got the numbers, let him challenge.
"Kevin hasn't got the numbers to challenge. He's well short of anywhere near a majority. He can't win."
The Australian newspaper reported that in the 103-member Labor caucus, Gillard currently had the support of 51 MPs while 31 were behind Rudd with 21 undecided.
In a separate interview with Sky News, Crean said the dispute was "starving Labor of oxygen".
"This has got to end," he said.
Rudd on Sunday denied he was preparing a challenge but also insisted he was a changed man and had learned to be less controlling and to consult more broadly -- two key criticisms that saw him lose office.
His comments came as a video emerged showing him in an expletive-ridden rant about a Chinese interpreter.
The two-minute video, uploaded onto YouTube by a user calling themselves "HappyVegemiteKR", shows an irate Rudd trying to record a message in Mandarin and railing against the interpreter who wrote the text.
Gillard's office denied leaking the expletive-ridden footage.
Several of Gillard's ministerial colleagues, meanwhile, threw their support behind her Monday, including Education Minister Peter Garrett, Defence Minister Stephen Smith and Trade Minister Craig Emerson.
"There is a campaign on here and it's a campaign that is anti-Labor, it's against the interests of the government of Australia and it's against the national interest and it should stop," said Emerson.