The last time they met was at the national day of memorial service in Christchurch, following the terror attacks on March 15.
Ardern had to postpone her planned trip to Australia, which was scheduled later that month, because of the shootings.
This is the third time the pair have met this year. Their meeting on Friday is an informal talk and not an official bilateral meeting.
Speaking to the Herald, Lowy Institute research fellow Natasha Kassam said Ardern would "absolutely" be well received by Australians during her visit.
"Australians particularly hold Prime Minister Jacinda Ardern in high standing," Kassam said.
A recent poll from Lowy showed that nine in 10 Australians say they have confidence in Ardern to "do the right thing in the world".
"That places her far ahead of any other world leader, including many of Australia's own leaders."
Asked why she was rated so highly, Kassam said it was because Australians respond well to leaders that are "warm and tolerant".
"I think for Australians, Ardern represents a lot of Australians' values, including multiculturalism, democracy and tolerance."
Another Lowy Institute poll found that a majority of Australians see New Zealand as its closest friend – far ahead of both the UK and the US.
Kassam said how New Zealand and Australia could work together in the Pacific would likely be on Ardern and Morrison's agenda.
As would conversations about China, given both Australia and New Zealand both have strong relationships with the country.
"There are times in which Australia looks to New Zealand to support some of its more difficult decisions."
Former chairman of the Australia New Zealand Business Council Kerry McDonald said outwardly, the relationship between the two countries was good.
But he said there was not a "depth of engagement" when it came to the political level.
Often, he said, politicians meet briefly and have a photo op – but conversations need to be much longer if lasting change is to be made.
"New Zealand has a long way to go before it gets the relationship with the depth and quality that it needs with Australia."
McDonald said Ardern needs to go into her meeting with Morrison with a firm list of priorities, particularly to do with economic matters.
He said Ardern's meeting with Morrison needs to be more than a photo-op.
When it comes to her speech to business, McDonald said the onus would be on Ardern to show how New Zealand is open for business and what her Government is doing to demonstrate that.
