MINING magnate and government critic Clive Palmer has questioned the role of Governor-General Quentin Bryce in determining whether Julia Gillard or Tony Abbott is allowed to form a government.

Ms Bryce's daughter Chloe Bryce is married to ALP powerbroker Bill Shorten, who was instrumental in Ms Gillard toppling Kevin Rudd for the prime ministership.

Chloe Bryce and Bill Shorten on their wedding day in November last year.

''We need to make sure that the Governor-General is totally impartial,'' Mr Palmer told The Age. ''If the Governor-General finds she can't be impartial, she should stand down and they should get someone else to fulfil that role.''

A spokeswoman for the Governor-General would not be drawn. ''The Governor-General does not comment on political matters,'' she said. Mr Shorten did not return calls.