While the government was pushing the Senate last week to back legislation for a lifetime ban on resettled refugees coming to Australia, he told Sky News that the issue was largely "hypothetical".
The leaders did not say whether the deal includes Australia agreeing to take in any US -held refugees in Costa Rica, where a similar situation has developed from people fleeing violence in South America attempting to reach the United States.
Turnbull said on Monday the first refugees to be resettled in the USA would not come before the January 20 inauguration of President-elect Trump.
Turnbull said Australia has launched a massive naval fleet in anticipation of people smugglers seeking to exploit news of the deal by marketing boat journeys to desperate asylum seekers.
"Our two nations, Australia and the United States have had a long co-operation on matters of this kind which have enabled us to pursue and support our mutual and respective humanitarian and indeed national security objectives", he told the Seven Network.
"We have a very long history of cooperation with the United States", he said.
The government has also announced it will set a permanent annual humanitarian refugee intake at nearly 19,000 a year, up from less than 14,000.
However, The Wall Street Journal noted on Friday that at least one Australian newspaper had predicted that a deal could be announced as soon as this weekend, while a source within Australia's immigration office told the American daily that both the U.S. and Canada were involved in talks with Canberra.
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Such trenchant proposals may strike a chord with those faithful to Les Republicains but risk alienating swathes of other voters. He faces a second-round vote against another former prime minister, Alain Juppe , who trailed him by 15 percentage points.
The prime minister restated the government's commitment to preventing asylum seekers who attempt to come to Australia by boat from being allowed to resettle here.
Immigration MinisterPeter Dutton has refused to be drawn on specifics, but earlier this week he stated that he is in "sensitive discussions with a number of countries" to relocate refugees from Manus and Nauru in a third country.
This image, taken on April 30, 2016 in Sydney, Australia, shows rights activists taking part in a candle light vigil for the refugees who set themselves on fire on the remote Pacific island of Nauru.
Turnbull said the most vulnerable refugees would be given priority. Very few refugees have taken up the offer of resettlement arrangements made with Cambodia and Papua New Guinea.
Immigration Department Secretary Chief Michael Pezzullo told a parliamentary committee on Friday that "today we are closer than we were yesterday" to resettling asylum seekers from Nauru and Papua New Guinea.
There seemed no short-term hope for asylum seekers on Papua New Guinea's Manus Island, a male-only camp holding 873 men.
Mr Adeang said refugees need to know they have a pathway to rebuild their lives and he expects a positive response from them. While those who are offered the USA move but reject it themselves would be offered a 20-year Nauru visa instead.
Opposition Leader Bill Shorten said Labor had not been briefed on the agreement, but welcomed the announcement. Remember, they neglected our borders, they allowed 50,000 unauthorised arrivals, they oversaw while they were in Government, 1,200 and more deaths at sea and it was the Labor Party that put these people on Nauru and Manus.