Julie Bishop has formed a strong working relationship with US secretary of state Rex Tillerson, and is hopeful he will not be ousted by the Trump administration as reports suggest.

It is understood CIA Director Mike Pompeo has been earmarked to replace Mr Tillerson, and while the foreign minister has had positive dealings with Mr Pompeo in his role at Langley, she says Mr Tillerson has her full support.

"I think he has represented the United States' interests exceedingly well, particularly in our region," Ms Bishop told Sky News today.

"I would hope that he would stay on. He's built up a lot of trust and respect in Australia and the Indo-Pacific."

He's built up a lot of trust and respect in Australia and the Indo-Pacific.

Having had "very productive" discussions with Mr Pompeo in the past, the deputy leader of the Liberal party insists a change to the senior White House diplomat position won't undo the progress made between her and Mr Tillerson.

"I feel sure that I could work closely with whomever the United States administration determines should be the secretary of state," she said.

Asked about Mr Tillerson's future, Mr Trump could only say — "He's here. Rex is here."

Adding fuel to the speculation, Mr Trump's press secretary Sarah Huckabee Sanders emphasised the point that what the President wants, the President gets.

"When the president loses confidence in someone, they will no longer serve in the capacity that they're in," she said.

Mr Tillerson and the President have seemingly been at odds for some time.

Although he has since denied it, the secretary of state reportedly called Mr Trump "a moron" after a meeting at the Pentagon in July this year.

They have also disagreed on how best to manage the Iran and North Korea situations, with Mr Trump tweeting that Mr Tillerson was "wasting his time" trying to negotiate with Kim Jong-un.

Pundits believe Mr Trump would have already instructed his chief of staff John Kelly to begin the transition, and have Mr Pompeo in place in the next couple of weeks.