Mental health issues may have been a factor, CNN said, citing the sources.
The location of the incident is not in close proximity to the West Wing or the presidential residence, reported CNN.
Witnesses saw a commotion on the White House grounds as security officers responded.
And still, both Trump and Turnbull both hammered home that the relationship between Australia and the United States can only grow exponentially.
Trump and Turnbull met earlier at the White House for talks on North Korea, with Turnbull expressing support for United States sanctions and economic ties.
The "mateship" - as the Australians have termed the longstanding alliance with the United States - was strained in the early days of the Trump presidency, with the USA leader critical of a program to accept refugees turned away from Australia.
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"The relationship with have with Australia is a terrific relationship and probably stronger now than ever before, maybe because of our relationship, our friendship", Trump said.
And despite a rising tide of isolationism, Mr Turnbull argued that the United States was at its best when it was acting as a global leader.
Mr Trump said in a tweet he was "honoured" to welcome the Turnbulls to the White House.
The two leaders discussed North Korea, with Turnbull expressing supported for USA sanctions and economic ties.
"What a great example of a hundred years of mateship", he said, referring to when the USA and Australia first fought together in World War I. "That leadership has been critical", Turnbull said.
"I look forward now obviously to working with the new leader of the National party who will be elected on Monday", Turnbull said.
Work on Afghan Section of TAPI Gas Pipeline to Begin Friday
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One America News was the first to be called during the press conference, with White House Correspondent Trey Yingst asking about the Parkland shooting as well as Syria. Trump praised Australia's point-based immigration system - implemented in 2016 - as one that must be mirrored by the United States.
However, they did differ on the Trans-Pacific Partnership and gun control.
From the moment Trump strode out to greet Turnbull on the South Lawn and they shared a side-by-side stroll along the colonnade to the Oval Office, it was clear the pair were ready to put on a show. "It may be very very unfortunately for the world".
Trump, a harsh critic of China's trade policies, named U.S. Pacific Commander Admiral Harry Harris, known for his hawkish views on Beijing's military expansion, earlier this month as the next U.S. ambassador to Australia.
Affirming their support for global health security to prevent, detect, and respond to infectious disease outbreaks, the two countries also agreed to intensify cooperation to support the growth of digital trade between them, ensure an open, free and secure Internet, and advocate the liberalisation and facilitation of global digital trade.
United Nations approves resolution demanding 30-day cease-fire in Syria
Starting Monday, pro-government forces carried out repeated raids on Eastern Ghouta, a suburb of the capital Damascus. The resolution aims at ending the carnage in the eastern Ghouta district and elsewhere in Syria .