A decision not to back Kevin Rudd's nomination to lead the United Nations would show the right wing of the coalition has the prime minister and foreign minister on a short leash, says Labor.
The federal cabinet is due to discuss on Thursday whether or not to endorse the former prime minister putting his name forward to be the next UN secretary-general.
Mr Turnbull insists it's not high on the agenda, but agreed with Alan Jones on 2GB radio that a nomination was a sign of indirect support.
Foreign Minister Julie Bishop told a meeting of coalition MPs in Canberra cabinet would decide whether to support his nomination, but it wouldn't be an endorsement.
She has since said Mr Rudd is "qualified" to be a candidate, given he is a former prime minister.
Acting Labor leader Tanya Plibersek told reporters in Sydney there were few people more qualified to lead the UN than Mr Rudd, given his diplomatic experience.
"If the cabinet today decides not to offer its endorsement to Kevin Rudd it will show that the petty, small-minded, Right wing of the Liberal party have Malcolm Turnbull and Julie Bishop on a short leash," she said.
Ms Plibersek said Ms Bishop had the ability to judge whether it was right to make the endorsement and the cabinet should back her.
Some of Ms Bishop's colleagues have been less enthusiastic, with Treasurer Scott Morrison reminding Labor it didn't help Peter Costello when he was interested in a role with the International Monetary Fund.
Veteran Liberal Eric Abetz is hoping cabinet will not back Mr Rudd, citing past Labor assessments of the former leader as a "narcissist, a micro-manager, an impulsive control freak and a psychopath".
"Any cursory glance at Mr Rudd's temperament and capacity would show that Mr Rudd is poorly qualified for this role," Senator Abetz said in a statement.
"If Australia were to seek to inflict Kevin Rudd onto the United Nations, it would be a mistake."
Cabinet minister Sussan Ley said she had no personal opinion on whether or not to back Mr Rudd but insisted there would be "vigorous" discussion.
"There are lots of views around the table," she told reporters in Canberra.
"I'm happy to listen to the lead from my colleague, Julie Bishop the foreign minister, and pick up the discussion from there."
