The Western Australia (WA) Senate result is likely to be challenged in court after the Australian Electoral Commission (AEC) revealed last week thatbetween the initial count and a recount.
The High Court sitting as Court of Disputed Returns could order a new election to be held.
It's unclear whether any new poll would be restricted to the same parties and candidates that contested the September 7 federal election, or if the regular procedure for nominations would occur.
Assange contested a Victorian Senate spot for his WikiLeaks Party in September, and attracted almost 41,700 primary votes out of 3.5 million.
But the WikiLeaks lead candidate in WA, Gerry Georgatos, said Assange would head the party's ticket instead if a new election were held.
This would allow Western Australians to "remedy the injustice of Julian Assange not being elected to the Senate" in the Victorian contest, he said.
"If a fresh election is called for, the WikiLeaks Party will contest the election and we will accept the will of the people, not the mistakes of the AEC," Georgatos said in a statement on Monday.
"The imperative is for Julian Assange to reach our Senate and to renew democracy, to break down the narrow corridor of political discourse that are we mired within."
Assange has been in the Ecuadorian embassy since June 2012 after seeking refuge there to avoid extradition to Sweden for questioning on allegations of sexual misconduct.
He had feared that the Swedish proceedings could result in him be extradited to the US, where there has been uproar over the decision by WikiLeaks to publish highly sensitive government cables and documents.