"The Saudi state security has visited my sister in prison recently. They have asked her to... appear on video to deny the torture and harassment," her brother Walid al-Hathloul, who is based in Canada, said on Twitter.
"That was part of a deal to release her."
There was no immediate reaction from Saudi authorities and the kingdom's media ministry did not respond to requests for comment.
Hathloul, who recently marked her 30th birthday in jail, is among around a dozen prominent women activists who are currently facing trial after being detained last year in a sweeping crackdown on dissent.
She was among a few detainees who accused interrogators of subjecting them to torture - including electric shocks, flogging and groping in detention - a charge vigorously denied by the government.
Hathloul also accused former royal court media advisor Saud al-Qahtani of threatening to rape and kill her, according to her family.
Her brother said she had initially agreed to sign a document denying that she had been tortured, as a precondition for her release.
He added that her family had intended to keep the deal secret.
But state security officials recently visited her again in prison to demand a video testimony.
"Asking to appear on a video and to deny the torture doesn't sound like a realistic demand," Walid tweeted.
Her sister Lina al-Hathloul separately said her sibling was under pressure to deny the torture claim.
"(I don't know) what I'm risking by writing this. Maybe it will harm my sister. But I can't keep it to myself," Lina wrote on Twitter.
"Loujain has been proposed a deal: deny the torture and she'll be free.
"Whatever happens I am certifying it (one) more time: Loujain has been brutally tortured and sexually harassed."
Hathloul's siblings have previously complained they were pressured by people close to the Saudi state to stay silent over her treatment in detention.
Riyadh has faced pressure from Western governments to release women activists, most of whom were jailed last summer just before the historic lifting of a decades-long ban on female motorists.
Many were branded as traitors by local media and are standing trial over charges that include contact with foreign media, diplomats and human rights groups.
Their trial has cast a spotlight on the human rights record of the kingdom, which has also faced intense global criticism over the murder of journalist Jamal Khashoggi in its Istanbul consulate last year.
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