In a Cabinet meeting that went well over time on Thursday, Mr Rudd's case was pushed by Foreign Minister Julie Bishop and supported by Attorney-General George Brandis.
The backing of some other ministers who spoke in favour has been described as lukewarm.
But many spoke against nominating Mr Rudd, including Immigration Minister Peter Dutton, Treasurer Scott Morrison and Finance Minister Mathias Cormann, who argued he was unfit for the role.
In the end it was left to the Prime Minister to make the call with the undertaking the leadership will support his decision.