Mr Stewart said while the on-going investigation "has it challenges", like all other investigations, it was like "every investigation".

The Cook MP's former partner, who raised the historical allegations in a letter sent to several MPs  asking for help in obtaining child support owed to her, will appear on A Current Affair on Thursday evening.

In a promo for the segment, the woman said Mr Gordon was "like a monster".

In a statement released on Thursday morning, Mr Gordon said he would not comment further on the allegations until the police investigation was completed.

"I note the kangaroo court known as A Current Affair will air a segment about me tonight.

"Unlike that program and other media outlets, I respect the current police investigation into certain allegations against me.

"I will thus make no comment until it is completed.

"Meanwhile I will continue to work hard on the issues that matter to my constituents."

Premier Annastacia Palaszczuk moved to sack Mr Gordon from the Labor Party for what she said was his "dishonesty" in not coming clean to her about whether there were any other issues in his past the party needed to know of, other than those raised in the letter his former partner had distributed.

Ms Palaszczuk said Mr Gordon said there was not any hidden issues and then later his criminal history, which was protected under the Rehabilitated Offenders Act, became known.

Mr Gordon quit before the party sacked him but maintains his seat as an independent. He has indicated he will continue to support Labor, as he was elected by his constituents as a Labor MP.

The LNP has continued to use the issue to put pressure on the minority-Labor government.

"There are a lot of questions that should be answered in regards to the Member for Cook," Mr Springborg said on the ACA interview.

"If the member for Cook misled the house, then the Parliament can deal with that.

"I am similarly concerned that the Premier stood up when she answered her very first question as Premier of Queensland, indicated that this matter had been properly dealt with and there had been a full and frank explanation, particularly in relation to the issues of the non-compliance with the rules around tax return and also child support.

"Now I understand the allegations continue from Billy Gordon's former partner continues to be that he has not paid his child support. Now, what basis did the Premier use when she eye-balled him to actually work out if he actually told her the truth, if he actually paid his child support?"

Ms Palaszczuk said Labor State Secretary, Evan Moorhead, had "assured" her, that he had followed her orders to rectify the situation, once she became aware of the child support and tax return allegations made in his former partner's letter.

Mr Gordon stood in Parliament on Friday, March 27 and said some of the claims made in the letter were true, and some were not, but he had made efforts to fix the situation.

"As a result I have moved to immediately rectify my tax affairs, and I have also ensured that any outstanding child support payments have been made to my ex-partner so that I can put this issue beyond doubt," he said last month.

"It upsets me to stand in this House and divulge details of such a personal nature to members. I am a proud father; it is the most important job I will ever do."

Since the allegations became public, both Labor and the LNP have accused the other of using the issue of domestic violence for political gain. Each has also attempted to claim the moral high ground by how they acted after, with mud being thrown from both sides on which party knew what, and when.

Parliament resumes next month.

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