Hanson-Young's lawyer, Rebekah Giles, sent a letter to the Liberal Democrat senator on Wednesday saying he had defamed Hanson-Young by suggesting, among other things, that she "is a slut, shagging men indiscriminately".
Giles, a partner with Kennedys law firm, told BuzzFeed News that if Leyonhjelm didn't acquiesce to the demands made in the concerns notice within a week, she will file a defamation lawsuit on Hanson-Young's behalf.
The letter says the matter is aggravated by the fact Leyonhjelm knew he was making false statements to a mass audience that included Hanson-Young's family and young daughter "in order to hold her up to shame and disgrace", and his "hatred" of Hanson-Young.
The stoush between the two senators kicked off last week when Leyonhjelm told Hanson-Young she should "stop shagging men" during a Senate debate on whether women should be armed with pepper spray and tasers to curb violence.
After he made the comment, Hanson-Young called him a "creep", to which he replied "Fuck off".
Hanson-Young penned an op-ed for the Guardian saying Leyonhjelm should be held to account for his words. She said on Twitter: "The truth is, for years I have winced and tried not to flinch at innuendos, yesterday I decided to stop and call it out."
It snowballed further when Leyonhjelm made allegations about Hanson-Young's personal life on Sky News' Outsiders show, which were broadcast on a strap along the bottom of the screen by a young producer, who was subsequently temporarily stood down from her job.
Leyonhjelm continued on a media blitz and made appearances on several programs, repeating various comments about Hanson-Young which she says are completely false, have damaged her reputation, and caused her "substantial hurt, distress and embarrassment".
The legal letter, provided to BuzzFeed News, points to six separate statements Leyonhjelm made about Hanson-Young between June 28 and July 1.
The statements include interviews on Sky News programs Paul Murray Live and Outsiders, the ABC's 7.30 program, Channel Ten's The Project, and 3AW radio.
The letter also includes a media statement Leyonhjelm published on Medium.com and later posted on Facebook.
Hanson-Young alleges Leyonhjelm defamed her in these statements by suggesting that she "is a slut, shagging men indiscriminately", that she is a misandrist, and that she "dishonestly promotes the view for her own political gain that men are born guilty of hating women".
It also alleges that Leyonhjelm suggested Hanson-Young is a hypocrite by "holding views that amount to hating men while at the same time is a slut, shagging men indiscriminately".
The letter lays out a number of aggravating factors, claiming Leyonhjelm hates Hanson-Young, that he intended to damage her reputation with the statements, and that he knew they were false and published them to a mass audience including Hanson-Young's family and child in order to hold her up to "public shame and disgrace".
It also accuses Leyonhjelm of "malicious conduct" in continuing to make statements about Hanson-Young for his own "self-seeking publicity and self-aggrandisement, and persisting to do so despite widespread condemnation by prominent persons in the community and by the community generally".
Along with an unreserved apology and paying compensation, the letter asks Leyonhjelm to stop making defamatory statements about Hanson-Young and to not destroy any emails, texts, call records and so on relating to the statements he made about her.
BuzzFeed News has sought comment from Leyonhjelm.