To be sure, the size of Australia's shadow banking sector is puny, at around 6 percent of financial system assets, and is relatively smaller than in a number of large economies.
Non-banks account for about 1 percent of Australian mortgage lending which is dominated by the so called "Big Four" - Commonwealth Bank, Westpac, National Australia Bank and ANZ Banking Group.
The quartet together control more than 80 percent of the country's lending and deposits.
In a separate statement on Monday, Morrison and O'Dwyer said the government was also seeking to lift the prohibition on the use of the word 'bank', in a bid to make the sector more competitive.
"New entrants to the Australian banking market face a simple but significant obstacle - the prohibition on the use of the word 'bank'," they said. "This acts to discourage innovative new
players from entering the market."
Separately, local media is speculating the APRA will announce new capital rules for major banks this week as it moves to make them "unquestionably strong" in the event of another global financial crisis.