Prime Minister Scott Morrison isn't ruling out referring Home Affairs Minister Peter Dutton to the High Court over his eligibility to sit in parliament.
Mr Dutton is facing continued questions about his personal financial stake in two publicly-funded Brisbane child care centres.
The connection could potentially put the minister in breach of the constitution.
"I have been consulting with the Attorney-General and we are dealing with those issues within our internal processes," Mr Morrison told reporters in Sydney on Wednesday.
Peter Dutton was been sworn in as home affairs minister at Government House on Tuesday. Source: AAP
"I would not have appointed Mr Dutton to the important role he has without considering those matters."
Au pair visa decision questioned
Mr Dutton is also under pressure to answer questions about his decision to grant a visa to a third au pair facing deportation.
Labor has questioned if donations to state and federal branches of the Liberal party influenced his decision to help a French au pair into the country.
The au pair, Alexandra Deuwel, was reportedly returning to Australia to work with Adelaide-based pastoralist Callum MacLachlan, who is second cousin to AFL boss Gillon McLachlan.
She was originally denied a tourist visa because of concerns she was planning to work, but Mr Dutton used his discretionary powers to grant her a visa.
Documents from the Australian Electoral Commission show Callum's father Hugh MacLachlan has donated $150,000 to the Liberal party, including $30,975 in 2007-2008, $44,170 in 2012-2013 and $50,000 in 2015-2016.
Shadow Immigration Minister Shayne Neumann told the ABC, "the issues of whether a Liberal party donor or family members have called on the minister to assist them should be ventilated before a Senate inquiry".
"The degree of seniority in terms of intervention really needs to be explained ... It becomes more and more murky and more and more unusual, shall I say, about what's been happening in relation to this issue as events unfold."
Mr Dutton rejected Labor's claim that political donations may have swayed his decision.
"That is completely untrue," a spokesperson for Mr Dutton said.
"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."
On Tuesday, Mr Dutton said he reviews every visa case on its merits.
He said immigration ministers receive hundreds of inquiries each year on individual migration matters from members of the public, organisations, journalists and MPs.
"There are long standing intervention powers provided to ministers to consider and deal with these representations," Mr Dutton said.
"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."
Greens Senator Nick McKim and Mr Neumann both said earlier Tuesday Mr Dutton has some serious questions to answer.
Peter Dutton at Parliament last week. Source: AAP
"Labor expects the new prime minister Scott Morrison to ensure his minister fully cooperates with the Senate inquiry and its efforts to get to the bottom of these matters," Mr Neumann said.
Last week, Labor successfully moved to establish an inquiry into "allegations concerning the inappropriate exercise of ministerial powers with respect to the visa status of au pairs".
The upper house committee will investigate two separate decisions by Mr Dutton to overrule his department's denial of entry to two young women in 2015.
Additional reporting: AAP
