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.
Mr Turnbull said he wants to speak to Mr Rudd before announcing it.
"We've considered this issue and I owe Mr Rudd a telephone call before I say anything more about it publicly," Mr Turnbull told reporters in Parliament House.
A senior official has told the ABC the Government would look petty if it did not endorse the former Prime Minister.
It is a view shared by acting Opposition Leader Tanya Plibersek.
"I think it would be small-minded, I think it would be embarrassing for the nation, I think it would be misguided and I think it would be wrong," she said.
"It will show that the petty, small-minded right-wing of the Liberal Party have Malcolm Turnbull and Julie Bishop on a short leash.
"Malcolm Turnbull should have the courage to stare down the extremists in his own party and put the national interest first instead of putting his factional fears above the national interest."