The stoush also split the Centre Alliance senators, with Rex Patrick supporting the move against Senator Cormann but Stirling Griff abstaining, saying it was only designed to humiliate Senator Cormann and would have achieved nothing.

It is unclear why Senator Hanson changed her mind. She said she had spoken with Senator Griff, who was also "very concerned", but Senator Griff said he hadn't spoken with her. He had texted her but hasn't received a reply, he said.

On Tuesday evening, it looked as though the Senate was united in its push to suspend Senator Cormann for three weeks over his refusal to release the report by the head of the Prime Minister's Department, Phil Gaetjens, into the sports grants affair.

Labor, the Greens and the crossbench had all signed a motion to that effect. But by the time it was debated on Wednesday, Senator Hanson had changed her mind, saying the Senate was overstepping its power.

"I did sign that although it did disturb me," she told the Senate. "It sets a precedent in this chamber that upon reflection I don't believe we should continue with."

Senator Griff said while he wanted the Gaetjens report released, suspending Senator Cormann as the Prime Minister's representative in the Senate would not have achieved that.

It was a "very childish" move that would have "effectively sent Senator Cormann off to the naughty corner for three weeks".

"I'm not supportive of an action designed to humiliate a member of parliament which is what this motion is all about," Senator Griff said.

Senator Cormann said it was an abuse and an overreach of the Senate's power.

"In the 119 year history of the Australian Senate those proposed sanctions are completely unprecedented," he said.

If the Senate was able to remove a senator by majority vote, the House of Representative could do the same, he said, suggesting the Leader of the Opposition could be removed by majority vote and be unable to ask questions.

"That would be completely inappropriate and we would never do it," Senator Cormann said.

He continued to insist the Gaetjens report was a Cabinet document so the government could claim public interest immunity against releasing it.

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Mr Gaetjens, head of the Prime Minister's Department, wrote advice for Mr Morrison on the role of Nationals Bridget McKenzie in approving $100 million in sports grants before the last election. Senator McKenzie largely ignored the rankings given to projects by Sport Australia and instead drew up a spreadsheet of marginal electorates and electorates the Coalition was targeting in the election. In an explosive report, Auditor-General Grant Hehir found she had directed grants to those electorates.

Mr Morrison has refused to release Mr Gaetjens report on the affair, but says Mr Gaetjens found "no material difference between those that were marginal electorates and those that were not" and "he did not find evidence that this process was unduly influenced by reference to marginal or targeted electorates". The stark differences between Mr Gaetjens and Mr Hehir's findings remain unexplained.

Mr Hehir appears before a Senate inquiry into the affair on Thursday. Mr Gaetjens is also expected to be called. The inquiry, chaired by labor's Anthony Chisholm, includes Eric Abetz and Matt Canavan as the Liberal members.