The senate crossbench - the Centre Alliance, One Nation and Jacqui Lambie have lined up with the Greens and Labor to co-sign a motion that would strip Senator Cormann of his role for a month.
If it passes, he could no longer represent Prime Minister Scott Morrison in question time and could no longer answer questions on his behalf in estimates hearings.
Phil 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 Morrison has claimed public interest immunity in refusing to release the report, characterising it as a cabinet document.
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.
Labor Senator Katie Gallagher said the senate had called for the Gaetjens report to be tabled on several occasions but the government refused.
"The Senate is standing together against a government and a prime minister that seem to think that the established conventions of public accountability and transparency can be ignored," she said.
On Monday, Senator Lambie blasted the government as taking the senate for mugs.
Centre Alliance Senator Rex Patrick said the senate could force the issue if labor was prepared to show courage.
"In the end, parliament is supreme. The senate chamber will win this if it wants to," he said.