The Greens are calling for a parliamentary inquiry into a "secret deal" involving Attorney-General George Brandis and the West Australian Liberal Government over funds from Alan Bond's failed Bell Group.

The deal would have given the WA Government preference as a Bell Group creditor over others including the Australian Taxation Office (ATO), which is owed $300 million.

Late last year, the WA Government passed legislation giving it the power to decide how to carve up a $1.75 billion Bell Group settlement, but the matter was quickly referred to the High Court over concerns it may have been unconstitutional.

According to a report in The West Australian, when those concerns were raised by a creditor in the High Court earlier this year, Senator Brandis instructed his then solicitor-general Justin Gleeson against running a particular argument effectively in support of those concerns.

But the deal was reportedly scuttled by Mr Gleeson, who wrote a scathing submission to the court on behalf of the ATO.

Australian Greens justice spokesman Nick McKim said if the claims about the Attorney-General were correct, it was a very serious matter.

"We've got a situation where if the reports are true, George Brandis has effectively instructed former solicitor-general Justin Gleeson to run dead in the High Court, and the effect of that of course would have been to deny the Commonwealth potentially up to $300 million of revenue that was due to the Australian Taxation Office," he said.

Allegations are 'the most serious' that Brandis has faced

Senator McKim said a parliamentary inquiry was needed to get to the bottom of what appeared to be a "very murky affair".

"Senator Brandis has run for cover here and we need to get him out of witness protection and into a Senate inquiry to answer these very serious allegations," he said.

"We'll be moving to refer this matter to the Legal and Constitutional Affairs Committee with a view to calling the Attorney-General to call former solicitor-general Justin Gleeson and potentially to call senior West Australian Government figures so that we can get to the bottom of this matter.

"We think the inquiry could be done rapidly and cleanly and report back in enough time for the Senate to consider this matter late in what will be the last sitting week of the year.

"I think these latest allegations are the most serious that George Brandis has faced in his political career, and that is really saying something because he has been a very trouble-prone Attorney-General."

The Opposition has called for Senator Brandis to be sacked over the claims.

However, Finance Minister Mathias Cormann dismissed the call, saying shadow attorney-general Mark Dreyfus and Opposition Leader Bill Shorten had a long history of "over-reach" when it came to the Attorney-General and were "just getting ahead of themselves".