Independent Senator Lidia Thorpe has quashed rumours she wants to rejoin the Greens, saying she has "no intention" of returning to the left-wing party.

In the lead up to the Greens' leadership announcement on Thursday, won by Larissa Waters, The Australian newspaper reported Senator Thorpe, who left the party in 2023 in part due to their stance on the Voice, was working with the Australian Greens' First Nations Network - also known as the Blak Greens - to elect Mehreen Faruqi as the party's new leader.

The article also argued "senior Greens figures" believed Thorpe was eyeing a return to the Greens, who will hold the balance of power in the Senate this Parliamentary term, however multiple sources told National Indigenous Times there was no truth to the rumours.

Following Senator Waters' appointment on Thursday, the Gunnai, Gunditjmara, and Djab Wurring Senator appeared on ABC Afternoon, saying there was no chance she would return to the Greens.

"Even if my daughter became the leader of the Greens, I would not join the Greens," Senator Thorpe said.

"I love being an independent. I get to decide what is best based on the Blak Sovereign Movement guiding me, and sometimes that does not sit well with the Greens, so I left with good reasons and good luck to them."

Senior leader and former co-chair of First Peoples' Assembly, Marcus Stewart, told The Australian people were "kidding themselves" if they didn't think Senator Thorpe has influence over the party.

The Nira illim bulluk man of the Taungurung Nation, who is married to ALP Senator Jana Stewart, said the 'Blak Greens' were a "handful of people claiming to be a movement of thousands".

"Thorpe has allegedly weaponised this group to undermine a competent senator in Dorinda Cox," he said.

In a statement on Thursday the Australian Greens' First Nations Network slammed the reporting in The Australian, labelling it a "conspiracy theory" and "baseless".

"The suggestion that grassroots First Nations members are incapable of making independent decisions is not only absurd – it is deeply offensive," the statement said.

"We are disappointed that so-called 'senior Greens figures' have chosen to spread conspiracy theories to Murdoch media outlets in an apparent attempt to advance their own personal agendas."

Appearing on ABC Afternoon, Senator Thorpe also said Australia needed a Minister for Indigenous affairs who would do more on the high suicide and incarceration rates for First Peoples in Australia.

"The minister [Malarndirri McCarthy] herself cannot answer questions in Question Time, she does not return the letters I have written to question her about what is she going to do about these damning rates," Senator Thorpe said.

The two have regularly sparred in the upper house, with Minister McCarthy telling Senator Thorpe in a fiery 2023 Senate hearing over police funding in the NT: "You are a disgrace to the Senate and you're a disgrace to your people."

Asked if she would do anything differently this parliamentary term, Senator Thorpe said she wouldn't, arguing, "I think I will continue to bring down the colony".

"I think I will continue to tell the truth, which justifiably hurts these politicians and the racists in this country," she said.

"So I will continue to be the activist that I am, and I will continue to fight for justice for my people."