"[I'm] afraid we are unable to share any more detail about the proposal because of the fact it is in consultation phase and owing to the privacy we must afford our people in regards to employment matters."
ANZ said it had no major restructuring plans right now. ASB also said it was not planning for "any material headcount adjustments".
Massey University banking expert David Tripe said all local banks were facing major challenges in maintaining large branch networks and BNZ's proposed changes could be related to that part of its business.
"One of the challenges that banks have with branch networks is that people come into them but they're not the people they're going to generate large amounts of business from," Tripe said.
Over 150 branches of New Zealand's major banks have disappeared in the past five years, and more are earmarked to go the same way.
Tripe said BNZ's changes were unlikely to be related to its call centre operations.
"I guess they could also be looking to do some more IT integration with Australia, but I wouldn't hold my breath on that one."
First Union, which represents around 25 per cent, said it had been reassured that none of its members were affected.
"But it's always concerning to learn people could be put out of work,"said spokesman Morgan Godfery.
BNZ currently has 4500 permanent full time staff and 760 permanent part time staff.
It reported a 16 per cent drop in profit for the six months to March 2016.
That decline in half-year profit - from $536 million to $451m - was mainly due to lower gains on financial instruments, affected by a falling kiwi dollar.
The local unit of National Australia Bank is due to report its full-year results on October 27, along with its parent.