The union's construction division was last year forced into administration by the Albanese government after allegations were made of bikie figures infiltrating the union and other criminal activity.
Administrator Mark Irving KC, reportedly ditched two anti-corruption teams hired to uncover misconduct in the union, according to Nine newspapers.
Other issues raised in Nine's reporting include a lawyer brought on to run the investigation quitting just weeks into his appointment due to concerns over inadequate powers.
Liberal senator Maria Kovacic will on Tuesday move to establish an inquiry into the CFMEU's administration.
She said it was an "absolutely necessary step" and said Labor had remained silent on what was taking place.
"The government can do one clear thing tomorrow to show that it's going to be transparent in relation to the CFMEU, and that is to not block the Senate inquiry," Senator Kovacic told reporters in Canberra on Monday.
"If they block that Senate inquiry tomorrow, it reinforces ... that they are not just looking the other way, but they are very much allowing the corruption in the CFMEU and elements of criminal conduct to continue."
Opposition industrial relations spokesman Tim Wilson said Mr Irving needed to front up before the parliament.
"So far they've avoided the parliament, it's time that we had proper oversights, proper scrutiny and proper action, because the allegations ... go directly to the government itself," he said.
"It's very hard to see how the CFMEU is going to be fixed when you have an administrator in place that seems to be running interference to protect the existing power structures."
The High Court in June dismissed a case brought by the CFMEU which attempted to overturn the federal government's decision to place the union's construction division into administration.
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