The inquiry into Peter Dutton's involvement in the au pair saga has made its findings.

A Labor-dominated Senate committee has found Home Affairs Minister Peter Dutton misled parliament when he said he had no personal connections to the employer of an au pair to whom he granted a visa.

He now faces a no confidence vote in the lower house on Thursday and a possible censure motion in the Senate.

The committee also found Mr Dutton only found out about two detained au pairs due to personal connections who contacted his office.

“There is no basis for the minister to be able to say that he had no personal connection, when the very genesis for this request came through his office because of his personal connections,” committee chair Senator Louise Pratt told parliament on Wednesday.

But Liberal senators on the committee said it was a “shambolic” inquiry that had failed to land a killer blow.

“The extensive hearings show that not only is there no smoking gun, there is, in fact no gun,” Senator Jim Molan said in parliament.

Hours before the report was released, Mr Dutton said the inquiry was politically motivated and predicted it would find him to be a “bad person.”

“It will be a political report with political recommendations,” he told reporters.

Internal emails show Mr Dutton’s office demanded an au pair detained at Brisbane airport be given urgent consideration for a visa, preferably within an hour.

Mr Dutton told parliament he did not know the people she was planning to work for.

It was later revealed her intended employer was an old Queensland Police colleague of Mr Dutton’s, Russell Keag, who emailed his office to say it had been a “long time between calls” but he needed help.

Mr Dutton said he had not spoken to Mr Keag in 20 years before he was approached for help with the visa.

The emails also show the department expressly disagreed with Mr Dutton’s push to give a visa to another au pair detained in Adelaide in November 2015.

He intervened after AFL boss Gillon McLachlan had his office contact Mr Dutton’s office to ask for help.

Mr Dutton pushed ahead with it anyway, and his ministerial decision had to be backdated after he missed signing it in time.

The committee recommended the Senate censure Mr Dutton.

Mr Dutton also faces a potential motion to refer him to the High Court over a possible conflict of interest due to his stake in two childcare centres that get Commonwealth funding.

Opposition Leader Bill Shorten said everybody from Malcolm Turnbull to Julie Bishop to the solicitor-general acknowledged there was an arguable case against Mr Dutton.

“There is a cloud of constitutional eligibility hanging over the minister’s head,” Mr Shorten said.