"I am fully qualified to take part in this competition," Khelif said after her win. Photo: Getty Images

The Algerian boxer won gold in Paris, despite being disqualified from last year's World Championships by the International Boxing Association (IBA), after she was reported to have failed gender eligibility tests in 2023.

However, the International Olympic Committee strongly defended Khelif's right to compete and ruled her to be eligible.

Her lawyer Nabil Boudi told Variety on Tuesday, that Musk and Rowling would be named in the lawsuit, following comments they made on social media.

Khelif's participation was widely discussed online, after Italian boxer Angela Carini abandoned her Olympic bout against her after 46 seconds.

Paris public prosecutor's office told news agency AFP on Wednesday that they had launched a cyberbullying probe, following a complaint by Khelif.

However, a prominent French legal blogger wrote on X that it is unlikely Mr Musk or Ms Rowling would face prosecution, as French penal law doesn’t apply to acts committed outside of France against foreign nationals.

But prosecutors could press charges against those who sent messages on French soil.

Khelif, along with Taiwan's Lin Yu-ting, was cleared to compete in the women's boxing in Paris, having been disqualified from last year's Women's World Championships for failing to meet eligibility criteria.

But the IOC took a different view, strongly defending the two boxers.

"This is a question of justice: women must be allowed to take part in women's competitions. And the two are women," IOC president Thomas Bach said.