The Australian Greens say they have dropped their investigation into claims made by former staffers against Western Australian senator Dorinda Cox, on the grounds she has left the party to join the ALP.

However, former Greens, now independent, Senator Lidia Thorpe has revealed a complaint she made against her former colleague is also unresolved.

Senator Cox, who held the Greens First Nations portfolio, announced her decision to defect to Labor on Monday.

WA Greens state director Dean Smith told the ABC on Tuesday the party's internal investigation of bullying claims surrounding the Yamatji-Noongar senator had not been resolved, but on Thursday the national broadcaster revealed party sources say the probe cannot continue.

Senator Thorpe, a Gunnai, Gunditjmara and Djab Wurrung woman who represents Victoria, said her complaint was lodged three years ago and made no progress because Senator Cox was unwilling to engage in mediation.

Prime Minister Anthony Albanese said on Monday that the allegations against Senator Cox had been "dealt with".

Questions from the ABC to Senator Cox were directed to Mr Albanese's office, which has not responded.

Senator Cox had previously issued an apology after multiple staff complaints.

"I take responsibility for any shortcomings in what has occurred during this period and I apologise," she said in October last year.

"Politics is a challenging and high pressure environment, especially as a First Nations Woman with five federal portfolios and competing priorities… There have been many challenges during my first three years in office including the COVID epidemic, taking on the First Nations portfolio alongside the Voice Referendum and leading many significant Committee inquiries."

Trish Frail, a Ngemba woman and co-secretary of the Australian Greens International, told the ABC the party would work to ensure there is Aboriginal representation at the federal level, given the departures of Senator Thorpe in 2023 and Senator Cox this week left the federal parliamentary party with no First Nations members.

Ms Frail added she was "shocked" by Senator Cox's defection.

"We got a five-minute warning," she said.

"I sent her a message… just saying I was disappointed, however wishing you all the best."