The Cook MP, who has stated his intention to stay on as the Member for Cook, has been on sick leave since having eye surgery to repair a detached retina shortly after his time as a Labor MP imploded.

He quietly re-opened his electorate office on Friday and has met with traditional owners over the proposed bauxite mine at Aurukun, an issue on which he has support from the two Katter Party MPs.

Mr Gordon will ask the Palaszczuk Government to implement an independent review into the "legal and administrative processes that have been undertaken by the Newman Government to ensure transparency, accountability, integrity and respect for indigenous rights" in relation to the mine, which he claims "has favoured Glencore and excluded the Wik and Wik Way people".

Speaking at a press conference on Monday morning, Premier Annastacia Palaszczuk said she saw no barriers to working with Mr Gordon on the cross benches.

"I will govern as if I have a majority of 20 and that means dealing with members equally, that means if they want briefings, if they want to talk to members of my government, we will deal with everyone equally, whether they are a member of the Katter Party, whether they are in Opposition, which is something we did not see during the past three years, under the former LNP government," she said.

"They are there to represent their constituents, he is there to represent his constituents of Cook, and I expect him to do that job just as every other member does."

The Opposition had called for a change to parliamentary standing orders so it could know which way Mr Gordon intended to vote and remove one of their own members from the chamber to "void" his support if it fell their way.  Labor refused.

An investigation into allegations he abused his former partner between 2005 and 2008 is on-going.

Under parliamentary rules there is nothing to stop him from remaining in parliament while police continue making their enquiries.  The rules that govern parliament also do not preclude Mr Gordon from sitting despite his admission he had failed to pay child support to his former partner or lodge tax returns.

He resigned  from the party ahead of being dumped for "dishonesty" last month after he failed to reveal his criminal history to the party.

Ms Palaszczuk said she had asked Mr Gordon if there was "anything else" in his past the party needed to know of following the domestic violence allegations and claims of missed child support and tax returns and was told there was not.

Mr Gordon's criminal history, which had been protected under the Rehabilitated Offenders Act, then became known.

Parliament resumes early next month.