Ministers at odds over Greens Senate deal

Two senior federal ministers are at odds over whether there's a deal with the Greens to push through Senate voting reform in the final week of parliament before a lengthy break.

Manager of government business in the Senate Mitch Fifield confirmed the government had struck a deal to secure "extra hours" to push through the bill in the week beginning March 14.

"The Greens have agreed to do that," Senator Fifield told ABC TV on Sunday.

But Attorney-General George Brandis - who is the government's Senate leader - says he hasn't seen commentary about a deal and is "not sure there is any truth to that".

By Senator Fifield's account the deal means the Senate won't get time to deal with legislation to restore the Australian Building and Construction Commission, seen as a double dissolution trigger.

"Part of that arrangement is that we can only deal with bills that (the Greens) are comfortable with," he said.

"So the ABCC will be dealt with in the sitting week after that."

Greens leader Richard Di Natale confirmed his party's commitment to passing the Senate voting reforms but admitted it came at a risk.

"It's been suggested that if we were to ... have a double dissolution ... the Greens is looking at potentially losing two senators," he told ABC TV.

There could already be a constitutional basis for calling a double dissolution election on the basis of the ABCC legislation - without it being formally rejected by the Senate.

The constitution specifies that a bill only must fail to pass the Senate twice to be an available trigger.

"The High Court has only once ... considered what constitutes a failure to pass," Senator Brandis told Sky News on Sunday.

"Let us wait and see."

The government already has two other double dissolution triggers available, including the registered organisation bill - which would establish a union watchdog.

Senator Brandis said that bill was "every bit as important" as the ABCC bill.

He said the Australian public knew "the need for reform of Australian industrial relations law, the need to restore lawfulness to the workplace, not just in the construction industry."