The coalition will push to set up a parliamentary inquiry into the administration of the CFMEU following serious concerns over its performance.

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 "abs

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