Failed Liberal leadership challenger Peter Dutton is under increasing pressure for intervening in visa cases of three au pairs, as questions linger over his eligibility for parliament.

The home affairs minister is facing questions about his decision to save a French au pair from deportation at the request of AFL boss Gil McLachlan, as revealed by Guardian Australia on Tuesday.

Two other interventions in visa cases of au pairs by Dutton are already the subject of a parliamentary inquiry.

As immigration minister in November 2015, Dutton used discretionary powers to free a 27-year-old woman from detention and grant her a tourist visa.

The au pair was planning to work for Adelaide-based farmer Callum MacLachlan, the AFL boss’ second cousin.

Callum MacLachlan’s father, Hugh MacLachlan, has donated roughly $150,000 to the Liberal party since 1999.

Labor wants to know if the donations influenced his decision to help the young woman into the country.

Dutton has flatly denied any wrongdoing and says donations had no influence on his decision.

“The minister has intervened in many cases presented by Labor members of parliament and you would have to ask them if they are presenting those cases based on donations to the Labor party,” a spokeswoman told the ABC.

In a statement on Tuesday, Dutton said “ministers for immigration receive, annually, hundreds of representations on individual migration matters from members of the public, organisations, journalists and other members of parliament”.

“There are long-standing intervention powers provided to ministers to consider and deal with these representations. These powers were the same under the former Labor government.”

“I consider cases on their merits. Any suggestions cases are determined on any other basis, including whether I knew the individual who referred the matter, is completely ridiculous.”

“There is an administrative process to be followed and it has been followed in every instance.”

Dutton, who last week made an aggressive push to become prime minister, is also facing questions about his financial interest in publicly-funded childcare centres.

Section 44 of the constitution bans people from parliament who have “any direct or indirect pecuniary interest with the public service of the commonwealth”.

Prime minister Scott Morrison isn’t ruling out referring Dutton to the High Court to test his eligibility.

“I have been consulting with the attorney general and we are dealing with those issues within our internal processes,” Morrison told reporters in Sydney on Wednesday.

“I would not have appointed Dutton to the important role he has without considering those matters.”

The opposition is demanding answers from Dutton on both matters.

“It looks like he’s got a good business in childcare and he seems to have a sideline in au pairs as well,” deputy Labor leader Tanya Plibersek told reporters in Melbourne on Wednesday.

Dutton defended his eligibility on Monday.

“I have conducted all of our affairs in accordance with the ministerial standards,” he told reporters. “I have declared any investments that we have, and if you’re making a suggestion otherwise then I’d like you to detail them.”

He also released legal advice confirming his eligibility, while the solicitor general found Dutton was “not incapable” of sitting in parliament but noted “some risk” of his being ineligible to sit under the constitution.