Ardern said that was an ongoing issue she would continue to raise.
"It will be one of many things we are likely to discuss. It is obviously difficult, but there are ongoing issues particularly as they relate to things like tertiary education. So it is important we keep having that dialogue."
The visit comes after a campaign in which now Education Minister Chris Hipkins became involved in a controversy surrounding then Australian Deputy Prime Minister Barnaby Joyce, and Ardern threatened to retaliate if university fees were hiked for Kiwi expats.
Hipkins' involvement drew an extraordinary response from Australian Foreign Minister Julie Bishop, who said she would find it "very hard to build trust with those involved in allegations designed to undermine the Government of Australia".
In response Ardern said she would welcome a phone call with Bishop. Today, she said they had not yet spoken, and she was unsure if they would meet during the Sunday visit.
"At this stage my understanding [is] that time only allows for brunch with Turnbull. I am of course open to meeting Bishop when we are able. I have no concerns about that, and it is likely to happen I'm sure soon."
Ardern said since becoming Prime Minister she had "plenty" of contact with Turnbull and Australian Labor leader Bill Shorten.
"There is no issue with our relationship with Australia."
New Foreign Minister Winston Peters has in the past called for New Zealand to apologise to Australia for not cracking down on people who use immigration to New Zealand as a "backdoor" or stepping-stone to Australia. Asked if she would make such an apology, Ardern said she there would be a wide-ranging discussion and she didn't want to pre-empt what would come up.
She had not met Turnbull before. Top of her agenda would be the looming Apec meeting and TPP11.
"The opportunity for bilaterals at Apec is often short. We have moments in time that we are able to grab around the fringes. This provides me an opportunity to have a longer conversation and with greater time between now and when we meet.
"TPP11 negotiations are underway now and in the lead-up to Apec. So this will be a useful chance for us to meet before then."
Ardern said she wanted to "build consensus around our negotiating position" with New Zealand First and the Greens.
Labour's plan to ban foreigners from buying existing houses would also come up in the meeting with Turnbull, Ardern said, but Australians would not be captured by such a ban, given they had the right to live here long-term.
Asked if she planned to apologise to Turnbull over Hipkins' involvement in the Joyce affair, Ardern said she did not, given Australian media had already made enquiries about Joyce's NZ citizenship, before Hipkins lodged written Parliamentary questions about citizenship issues.