Each of Australia's states is represented by 12 senators, with half-senate elections for some 40 vacancies generally held at the same time as national polls for the lower House of Representatives.
The "state Julian will run for will be announced at the appropriate time", WikiLeaks said.
The Australian government has previously blasted WikiLeaks, with Ms Gillard describing its release of US diplomatic cables as "grossly irresponsible".
Ms Gillard's government ordered Australian police to investigate whether WikiLeaks had broken Australian law, but they reported back in 2010 it had not broken any under their jurisdiction in releasing the cables.
Mr Assange is fighting being sent to Stockholm because he fears it would open the way for his extradition to the US to face charges of spying linked to the leaking of classified military documents by US soldier Bradley Manning.
Manning has been formally charged for allegedly turning over a trove of classified US documents to WikiLeaks in one of the most serious intelligence breaches in US history.
Wikileaks.org was set up by a group including Mr Assange, a former computer hacker, in late 2006 to let whistle-blowers post sensitive documents on the internet without being traced.
The group has since released thousands classified US military documents on the wars in Afghanistan and Iraq and more than 250,000 classified US diplomatic cables, many of which were deeply embarrassing to Washington.