The Taliban is actively seeking global recognition and has announced a new administration since its takeover of the war-torn country in August.
The militant group wants its spokesman Suhail Shaheen to be recognised as Afghanistan’s ambassador to the United Nations.
Despite insisting it had changed since the 1990s, where public executions and punishment were meted out, women were not permitted to hold office and girls were banned from education, the Taliban has been criticised for reverting back to some of its old ways.
In an interview with SBS News in Washington, Mr Morrison said it would "take a lot of convincing" for Australia to consider recognising the Taliban as a government.
"There'll need to be a lot of demonstrated performance from the Taliban before Australia starts moving in a direction that could give them any sort of legitimacy," he told SBS News in Washington.
Asked about the prospect of a Taliban representative occupying Afghanistan’s embassy in Canberra, Mr Morrison said: "That is something that is not in contemplation".
Afghanistan expert professor Amin Saikal says while it's still early days for the world to recognise the Taliban, it all begins with recognition by the UN.
"If the UN decides that, 'yes we will accept the Taliban representative to replace the current Afghan ambassador to the UN' because it's an international body, that will open the way for a number of other countries to do that," he told SBS News.
But he said some countries don't have to necessarily wait for the UN to go their own way, and there's speculation that China could be the first to recognise the Taliban.
Any potential Taliban representative in Canberra would be afforded diplomatic immunity under the Vienna Convention on Diplomatic Relations.
"By accepting the Taliban ambassador, Australia would be very clearly giving recognition to a Taliban government," Australian National University professor of international law Donald Rothwell told SBS News.
"Australia's being quite coy about not wanting to give formal de jure recognition to a Taliban government, so I think that's perhaps the most important step," he added.
"Boris Johnson very soon after the fall of Kabul to the Taliban was very keen on ensuring that there be a coordinated position amongst key western allies on this point, so it'll be interesting to know whether on the sidelines - either directly or indirectly - there was some discussion in Washington about these particular issues."
Mr Morrison said he would be discussing the issue of Afghanistan with allies in Washington, in particular about getting more visa holders and Australians out of the country.
"We've had a lot of discussions over this past week and we'll have one today, which is about pathways that we can get more people out of Afghanistan," he said.
"It's still very early days, and it's on the Taliban to be good to what they've pledged to enable people to leave if they wish to."
Mr Morrison also repeated earlier comments that there was no cap on the number of humanitarian refugee visa places for Afghans fleeing the Taliban takeover.
He said around 100 people have arrived in Australia under that refugee program so far.
"If it needs to be bigger, it'll be bigger," the prime minister said.
