Coalition legal affairs spokesman George Brandis said FWA officers should seek a meeting with the Commonwealth Director of Public Prosecutions (DPP) to ascertain what else it could do.
The DPP has said while it would consider the FWA report, it did not regard it as a "brief of evidence" gathered from a criminal investigation.
Senator Brandis said a brief of evidence would contain much of the same material as FWA should have used in its investigation.
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"Assuming that the documents ... have already been identified, a competent junior solicitor would be able to assemble that into a brief of evidence within days," he told Sky News.
"I think it would be a good idea if today or very soon the senior officers of Fair Work Australia sought a meeting with officers of the Commonwealth DPP and had a discussion about this."
Senator Brandis questioned why FWA continually had blocked attempts to scrutinise its investigation, including so far refusing to make the report public and giving the DPP a report "which is not serviceable to his needs".
"You could only conclude that Fair Work Australia are bending over backwards not to enable this process to go forward," he said.
