The office of the Prime Minister Bill English is trying to arrange a phone call with the United States President Donald Trump, after being contacted by the White House.
Deputy prime minister Paul Bennett says trade and climate change are likely to be discussed.
The call between the Australian Prime Minister and President Trump caused a great deal of controversy, after varying accounts about the nature and tone of the call, and after the President expressed his anger about a deal struck by his predecessor to take more than 1000 asylum seekers from Australian detention centres.
Details of the tense phone conversation with Malcolm Turnbull, which Mr Trump reportedly described as "the worst by far", were published by the Washington Post on Thursday.
Mr Trump reportedly accused Mr Turnbull of seeking to export the "next Boston bombers" to the US, and complained that the deal was going to kill him politically.
Mr Trump followed up the conversation with a tweet in which he railed against the "dumb deal".
Mr Turnbull said he was disappointed the details of the call, which he described as "frank and forthright", were leaked.
Last week, Mr English said he was not worried or nervous about his upcoming phone call with the United States President and he looked forward to it.
The office of New Zealand's Prime Minister said they were planning for a phone call today, but that could still change.
Speaking to reporters at Waitangi, Ms Bennett said she hoped the discussion would turn to climate change - and that the US would acknowledge their environmental obligations and do something about it.
Trump suggests some US leaders just as violent as Putin
Meanwhile, Mr Trump has raised eyebrows by saying the United States had a lot of killers, suggesting Russia's president, Vladimir Putin, was no worse than them.
He made the comments in an interview to be broadcast during the pre-game show of the annual Super Bowl football championship final, which is one of the country's most-watched television events.
In the interview, Fox News' Bill O'Reilly puts it to Mr Trump that Mr Putin was a killer, challenging Mr Trump's avowed respect for the Russian leader.
The president responds by saying the US had a lot of killers, and queried whether his country was so innocent.
Republican Senate majority leader Mitch McConnell reacted by saying the two countries were not comparable.