Prime Minister Malcolm Turnbull has fuelled speculation cabinet will sink Kevin Rudd's bid to lead the United Nations, rejecting Foreign Minister Julie Bishop's central argument in favour of the nomination.

In an interview ahead of Thursday's cabinet meeting, which will make a decision on the matter, Mr Turnbull argued the government's nomination of the former Labor prime minister would amount to support.

Ms Bishop, the main backer of Mr Rudd in cabinet, recently told the Coalition party room that a "nomination is not an endorsement" but the former Labor leader has not attracted the support of other senior ministers.

Treasurer Scott Morrison, Immigration Minister Peter Dutton, Industry Minister Greg Hunt and several backbenchers have publicly questioned the former Labor leader's merit and suitability to be secretary-general of the powerful international organisation.