Labor says it could support the creation of a Homeland Security-style super department that brings together Australia's intelligence agencies to fight terrorism.
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But senior opposition frontbencher Brendan O'Connor says greater parliamentary oversight of such an agency would need to be put in place.
There has been growing speculation in government ranks that Immigration Minister Scott Morrison could take on a super portfolio with additional responsibility for counter-terrorism once a government-ordered review of Australia's counter-terrorism machinery is concluded.
Some in government have also suggested Mr Morrison could also take on some of under-performing Defence Minister David Johnston's portfolio responsibilities, but Foreign Minister Julie Bishop is among those fighting a re-organisation of agency responsibilities.
Mr O'Connor, a former home affairs and immigration minister, said Labor had considered creating a similar portfolio under the leadership of Kim Beazley and then Kevin Rudd before coming to power in 2007.
He said the portfolio should not be created simply to satisfy the "ego and ambition" of Mr Morrison but added that "if you look at America, look at Britain, look at some of the European states and our Asian neighbours, it's the way they have gone".
"Labor has looked at these things, we didn't end up doing them. Anything the government put we would look at [but] the caveat is that parliamentary oversight is very important," he said.
"If you look at how stringent the parliamentary oversight is of agencies in Canada, Britain, I think and I would argue that it's stronger than we have had to date. So if you were going to go down that type of route, particularly in the hands of one minister, you would really want stronger parliamentary oversight."
Junior government frontbencher Steve Ciobo played down the prospect of an imminent reshuffle on Tuesday, arguing the government would make a decision on a re-organisation in Australia's national interest.
"We are not going to make a decision that suits a particular whim," he told Sky News.
"The government has ordered a review into the efficacy and operations of our intelligence and police services. I'm not going to get too worked up about media speculation about what is going to happen."
