Prime Minister Malcolm Turnbull dismissed advice from the Department of Foreign Affairs and Trade saying Kevin Rudd was qualified for a tilt at the UN chief job.
Mr Turnbull has said the government would not back the former Labor prime minister because he didn't believe he was suited for the role.
DFAT's submission to cabinet said Mr Rudd was a better candidate than previous secretary generals who held the job, The Australian reports.
Meanwhile a former Australian ambassador to China who served under the Rudd and Gillard government, Geoff Raby, says Mr Rudd's bid might not be over.
Mr Raby pointed out Mr Rudd was close to US Democrats presidential candidate Hillary Clinton.
In an opinion piece for the Australian Financial Review he speculated that Mrs Clinton could back him for the job, if she wins the US election.
Trade Minister Steve Ciobo denied the decision set a precedent.
"The reasons the prime minister harboured reservations have been laid out by the prime minister and I'm comfortable with it," he told ABC radio on Monday.
"It's not to be viewed as setting a precedent in any way, shape or form."
