While Albanese has only been in the job for little more than a month, he last month suggested openness to considering individual circumstances of New Zealanders in Australia with criminal convictions before deporting them to New Zealand.
The problem, from New Zealand's perspective, is that deportees don't always have social connections in New Zealand, which risks making them susceptible to joining gangs.
Ardern on Monday said providing Kiwis in Australia with smoother pathways to citizenship addresses a root cause of the deportation issue.
Nonetheless, Albanese will be heading into the meeting having spent time in Europe, where he was immersed in geopolitics and trade - all the while Sydney grappled with flooding.
Ardern said she will be looking to talk to Albanese about his recent visit to Kyiv.
She said she was interested in what he saw on the ground and what role he believes New Zealand and Australia can play in Ukraine's reconstruction.
Australia's Foreign Affairs Minister Penny Wong took a slightly different approach towards Russia's invasion of Ukraine in a speech she gave in Singapore, just ahead of Ardern addressing Sydney's Lowy Institute on Thursday.
Wong specifically called on China to exert its influence over Russia to end the war.
"The region and the world are now looking at Beijing's actions in relation to Ukraine," Wong said.
Ardern didn't single out China in the same way in her speech. But when media asked her about Wong's statements, she made a generalised comment about countries on the United Nations Security Council pressuring Russia.
She then went a bit further and said, "If that is China's position, then it's our view that they should too join with the international community in calling out Russia on its war in Ukraine."
Ardern, in her speech, tried to cauterise the war issue, saying it's "Russia's war" and not a war of "the West vs Russia" or "democracy vs autocracy".
Accordingly, she said we shouldn't assume "it is a demonstration of the inevitable trajectory in other areas of geostrategic contest".
Later on Thursday, Ardern spoke at an Australia New Zealand Leadership Forum event with Albanese.
The two-day forum brings together more than 250 New Zealand and Australian businesspeople and government representatives to share ideas on common economic and political issues.
Having just recovered from Covid-19, Finance Minister Grant Robertson made it to the forum, which is also being attended by ministers Damien O'Connor (trade), Stuart Nash (tourism), Willie Jackson (Māori development), Michael Wood (transport), Ayesha Verrall (Covid-19) and James Shaw (climate change).
Topics of discussion on the agenda include indigenous business, trade, the future of health, infrastructure, tourism, transtasman innovation opportunities, labour shortages, the future of work, economic growth challenges post-Covid, and climate change collaboration.
Australia is New Zealand's second-largest trading partner, with two-way trade accounting for over $22 billion in the year to December 2021.