"We are always interested in new gang movements when they enter a district and we will continue to gather and assess information as it comes to hand," a police spokesman said.
Police would not provide any further information.
In June, The New Zealand Herald reported the Finks had set up a chapter in New Zealand.
Formed in Adelaide in 1969, the Finks have chapters in several Australian states.
They also have a long-standing rivalry with the Mongols, after many members patched over to the gang about a decade ago.
Tensions between the two gangs flared up in Queensland in June, with an arson attack and brawl at the Gold Coast's Australia Fair Shopping Centre.
It is the latest Australian gang to arrive on New Zealand shores, in the wake of the Australian Government's 501 deportee policy.
Since the deportation policy was enacted in 2014, gangs such as the Comancheros, Bandidos, and Rebels have established themselves in New Zealand's organised crime landscape.
An increasing gang presence in the South was blamed when the Otago Daily Times recently reported the South had one of the highest rates of illegal gun seizures in the country.
New Zealand Police Association region seven director Grant Gerken, of Invercargill, said Southern, like many districts, was experiencing an increased gang presence.
With that growth came a corresponding upsurge in the presence of illegal firearms, he said.
"At one time, it was a perceived threat amongst our membership. Now, it's the reality, and alarmingly reflective of the increasingly dangerous environment police operate in."