The Dominion Post newspaper said the umpires are unhappy they have not received a pay increase in five years while players' earnings have rocketed since the advent of the Twenty20 format.
Umpires came close to striking during New Zealand's domestic Twenty20 competition but instead hired a professional negotiator to take their claims to New Zealand Cricket.
In a report citing leaked emails, The Dominion Post says negotiations are continuing but strike action is still a possibility.
Umpires have lowered their initial pay claim but NZ Cricket is still refusing to meet the new demand, reports said. NZ Cricket chief executive Justin Vaughan said negotiations were ongoing and it was inappropriate to comment further.
New Zealand's elite umpires panel comprises 10 umpires, including Tony Hill, who is standing in the second Ashes test between Australia and England in Adelaide, and test umpire Billy Bowden.
Panel members, apart from Hill and Bowden, are reported to earn around NZ$40,000 a year in retainers and match payments.
NZ Cricket's umpires manager, Rodger McHarg, refused to discuss the standoff but NZ Cricket Players' Association manager Heath Mills confirmed the dispute was continuing.
"I'm aware they are in discussions with NZC about their contracting environment and it's important they are looked after given the role they have in the game," Mills said.
He said a strike should be avoided at all costs.
"If they are talking about not umpiring that is not a good result for anyone and illustrates the relationship is not great and needs some work," Mills said.
"Hopefully, common sense prevails and NZC and the umpires get around the table and create some sort of contract or environment that everyone is happy with."
