The conservative politician's party is trailing behind the Queensland Greens candidate Penny Allman-Payne for the race to the Senate.
Senator Hanson, who had to spend election day in isolation after testing positive to COVID-19, was well short of a quota on Saturday night as counting continued.
Her party polled 7.8 per cent of the Senate vote, to the Greens' 14 per cent.
The outspoken Queenslander has run an anti-vaccine mandate campaign, and refused a coronavirus jab herself.
She was first elected to the Senate for Queensland in 2016.
In the Sunshine State, Nationals senator Matt Canavan was re-elected, as was his Victorian colleague Bridget McKenzie.
High-profile Liberal senator Simon Birmingham was also returned.
On the incoming Labor government's side Penny Wong, soon to be foreign minister, was re-elected for South Australia.
Senator Wong will need to be sworn in next week ahead of the Quad security meeting in Tokyo on Tuesday.
Labor senator Murray Watt was also returned to the chamber, while Queensland senator and former assistant minister for women Amanda Stoker is at risk of losing her position.
Senator Stoker, who was third on the Queensland LNP ticket, sparked controversy after attending an anti-abortion rally in Brisbane during the election campaign.
High-profile candidates Nick Xenophon and Clive Palmer fell well short of a quota in their SA and Queensland races.
Independent candidate and former Wallaby David Pocock is tipped to defeat outgoing minister Zed Seselja on preferences for an ACT Senate seat.
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