Prime Minister Malcolm Turnbull's own department has been forced to correct records showing a company he jointly-owned had been awarded a government contract, which could have raised questions about his election eligibility.

In June 2010, Mr Turnbull's wife Lucy was awarded an 18-month contract by the then-Labor government to consult on an expert COAG panel about cities.

A register of Department of Prime Minister and Cabinet contracts had noted the work was awarded to Turnbull & Partners, a family company jointly owned by Mr and Mrs Turnbull and which the Prime Minister serves as a director.

Fairfax Media inquired about the arrangement on Friday following revelations former Senator Bob Day's election to the Parliament might be ruled invalid because of a connection to government business.