Marise Payne says the government is making "appropriate enquiries" into the matters raised in reports by Nine's newspaper and television outlets.

"There are investigations underway broadly by law enforcement agencies into financially motivated crime and that includes ... the so-called casino junket operations," she told Sky News on Tuesday.

"But I would always say that Australia's posts should be used in an appropriate way, in a lawful way and observing all requirements and regulations in our work."

The government insists a past deal it struck with Crown Resorts to fast-track short-stay visa applications for clients did not involve any special treatment.

Nine on Tuesday claimed Crown was one of a number of big companies to have an arrangement with the immigration department to fast-track applications for short-stay visas through Australia's consulates and embassies.

While the Department of Home Affairs says there were fast-track visa arrangements, it denied this had led to preferential treatment, such as reduced vetting, for applicants including people from China.

"Our offices in China are well-aware of the risks that may be present in their caseloads and they scrutinise and manage applications accordingly," a department spokesman told Nine.

"These arrangements always make it clear that applicants are subject to the full range of applicable checks."

The short-stay visas arrangement involving Crown's clients began in 2003 under the Howard coalition government and continued under the Gillard Labor government in 2011, but ended in 2016, Nine reported.

An earlier report accused Crown of laundering large sums of money through its Melbourne gaming venue - allegations the casino giant has strongly rejected.

Crown executives could be hauled before a parliamentary inquiry with the Greens hopeful of winning support from Labor to send the affair to a committee for scrutiny.

The minor party believes the issues raised in the media reports amount to corruption.

If the inquiry gets up, Greens senator Nick McKim is also keen to bring former Border Force head Roman Quaedvlieg under its parliamentary privilege to give him protections to name the two ministers and an MP he claims helped smooth out border security for Crown's big gamblers.

Independent Tasmanian MP Andrew Wilkie also wants a parliamentary inquiry, although his motion in the lower house is expected to fail.

Labor is not ruling out backing an inquiry, but wants Home Affairs Minister Peter Dutton to explain what has happened.

The minister is in London for meetings with representatives from the Five Eyes security alliance.

"We need to actually hear from the minister about this," Labor deputy leader Richard Marles told ABC Radio National.

"It does relate to the relationship between Crown and the Home Affairs department through to Australian Border Force."

Australian Associated Press