Hours after England's defeat in Mount Maunganui, Archer revealed he had heard "racial insults" from "one guy" while returning to the pavilion in an incident that led to a wide-ranging inquiry from an apologetic home board.
The investigation included scrutinising CCTV footage, listening to audio, interviewing bystanders and obtaining material on social media - although Cricket has been unable to conclusively identify the individual.
However, New Zealand Cricket chief executive David White feels what it has gathered is enough to justify lodging a complaint with Tauranga Police.
"What happened to Jofra was reprehensible and has led to a general upscaling of security around the area of racial abuse at all our international venues," Mr White said.
"Should the person responsible ever re-offend, we believe we have enough information to link him to the Bay Oval incident."
New Zealand Cricket said it would not "comment on public speculation regarding his personal details", but if the perpetrator was identified, the governing body would seek to a ban "from all its international venues for a lengthy period".
Black Caps captain Kane Williamson labelled the incident "horrific" while White travelled to Hamilton - the venue of the second Test - to meet with and personally apologise to the fast bowler.