Previously, Ardern has given almost no indication as to who she thinks should be in the job next.
But she has ruled out former Deputy Prime Minister, and New Zealand First leader, Winston Peters.
Asked about the role at Waitangi earlier this year, and whether she thought Peters would be a contender, Ardern said she did not intend to appoint a former politician to the role after Dame Patsy's term ends.
The Governor-General is paid $371,900 a year and has a $33,358 annual allowance.
As well as this, they get a $79,000 annuity – a yearly pension-like payment.
The Governor-General's job is to be the Queen's representative in New Zealand.
The job includes reading any newly elected government's speech from the throne – a pre-written speech outline of the new government's policy intentions over the coming three years.
They also sign into effect any new laws in New Zealand, giving any legislation passed in Parliament the Royal Assent.