Professor Twomey told The Australian the Solicitor-General's opinion brings up information about funding for the child care centres owned by Mr Dutton's family trust which "raised considerably the risk of disqualification" under section 44 of the constitution.

This new assessment comes after Julie Bishop called for "clarity" over Mr Dutton's eligibility and backed former prime minister Malcolm Turnbull's calls for his referral.

Shadow Treasurer Chris Bowen told reporters in Sydney on Saturday that it was "very important" that Mr Dutton be referred.

"I see one of Australia's most eminent constitutional lawyers, Anne Twomey, suggesting today that the case for the reference to the High Court has been increased, is now stronger," he said.

Mr Bowen wouldn't say if and when Labor would make a second attempt to move a motion to refer Mr Dutton to the High Court, only that "we'll keep our options open."

Last week a Labor motion for a referral was defeated by just one vote.

Ms Bishop hasn't ruled out crossing the floor to support the motion, saying if a vote was called: "I will make up my mind at that time".

Crossbenchers Cathy McGowan and Rebekha Sharkie told The Conversation on Wednesday that they would vote for a referral.

Ms McGowan said, "it should be done quickly and efficiently and effectively and sorted out."

"I think it's taking up a huge amount of space in parliament at the moment," she said."

According to The Saturday Paper, Mr Dutton only absented from one cabinet discussion on child care, despite having regularly declared his family investments.

A spokesperson for Mr Dutton said: "The minister has complied with the Statement of Ministerial Standards and the Cabinet Handbook. Suggestions to the contrary are false".

Finance Minister Mathias Cormann told reporters in Perth there was no question Mr Dutton had been validly elected to the House of Representatives.

"This is a partisan campaign on behalf of the Labor party ... the Labour party is getting quite desparate here."

Australian Associated Press