Assange's wife Stella and his brother Gabriel Shipton will be in Canberra on Wednesday to lobby MPs for support in placing diplomatic pressure on America for a pardon to be granted during the dying days of the Biden administration.
A multi-partisan group of MPs had been instrumental in helping to raise the plight of Assange and secure his release from custody on espionage charges after years behind bars.
Mr Shipton said time was running out for a pardon to be secured before Donald Trump was sworn in as president in January.
"The parliament was integral to getting Julian out and they were the key to unlock his cell basically, and they can continue and finish the job and push for this pardon," he told AAP.
"There's a ticking clock going on for when the president can make the decision to pardon Julian."
Assange landed in Australia in June after he pled guilty to spying charges after leaking troves of secret state information.
He spent almost seven years holed up in Ecuador's London embassy before being detained at a maximum security prison in the UK where he fought his extradition to the US.
The US Justice Department had asked the UK to extradite Mr Assange in 2019, which was during Mr Trump's first term as president.
Mr Shipton said there was concern a pardon would not be issued with Mr Trump being back in the White House.
He indicated Prime Minister Anthony Albanese could hold significant sway with Mr Biden in securing a pardon for the WikiLeaks founder.
Gabriel Shipton is among the loudest voices calling for his brother to be pardoned. (Mick Tsikas/AAP PHOTOS)
"When (Albanese) was advocating for Julian, a lot of the firewall was on the separation of powers and that we could not interfere with the US Department of Justice process," he said.
"Now that the process is at a conclusion, it really is in the power of President Biden to unwind this precedent that originated with the Trump administration.
"(A pardon) would be a real coup for the prime minister."
Mr Albanese had previously raised the issue of Assange with the current US president, with federal MPs also lobbying US lawmakers.
The brother of the WikiLeaks founder said a pardon would be significant.
"Julian is a convicted criminal and was convicted for something that journalists do every day, and this is something the Australian government could be really proud of on the global stage," Mr Shipton said.
"Julian is pushing for a pardon, not just because it affects him, but because of what he stands for."
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