Independent MP Bob Katter has threatened to plunge the Morrison government further into minority by supporting the referral of Liberal MP Chris Crewther to the High Court to determine the Victorian backbencher's eligibility to sit in Parliament.

Declaring he was "not impressed" with the government and accusing it of "running around pork-barrelling", Mr Katter gave a clear sign his reliable support for the Coalition was now in doubt.

And in a further complication for Prime Minister Scott Morrison's relationship with the powerful and enlarged crossbench, newly elected MP Kerryn Phelps indicated she was open to referring Mr Crewther and Home Affairs Minister Peter Dutton to the High Court, pending legal advice.

Crossbench MP Bob Katter says he is considering referring Liberal MP Chris Crewther to the High Court. Credit:Alex Ellinghausen / Fairfax Media

Mr Crewther, a first-term MP who holds the seat of Dunkley in south-east Melbourne, faces referral over his shareholding in biotech firm Gretals Australia, which has received grants and funding from the Commonwealth.