"There are some anomalies now in the treatment of New Zealand citizens in Australia in terms of access to higher education...I think we need to actually bite the bullet and Australia needs to make a decision - do we want to support New Zealand permanent residents in terms of their access to higher education in Australia or are we going to treat them as second-class residents in Australia."
Shorten said he was also interested to hear Ardern's views about other matters in the region.
'"She is already showing, and many Australians will notice you are showing, global and regional leadership," he said.
But it seemed the dinner wouldn't be all politics with Shorten being handed an important order from his children.
"Jacindamania has spread across the Tasman. My daughters want me to get a selfie with Jacinda to send back to them."
The Prime Minister's weekend agenda also featured a photo shoot for fashion bible Vogue on Saturday. Ardern is set to feature in the March issue of the US edition of the magazine.
Ardern will not be on the cover – the magazine has never used a female politician on its cover although both Michelle Obama and Hillary Clinton were on the cover as First Lady to a President.