"New Zealand is in touch with Equatorial Guinea and is asking permission to board the vessels, if their flag status is verified," Mr McCully said.
The Government has asked Interpol to issue a "purple notice" for each vessel, which would alert their illegal actions to 190 member countries in an attempt to stop them offloading their catch at any port.
Mr McCully said the vessels were "well-known, repeat offenders" linked to Spanish interests.
"We have alerted the Spanish Government to what we have discovered," he said.
The New Zealand navy had gathered photographic and video footage of the vessels' illegal fishing, which would assist with legal action against the owners, Mr McCully said.
New Zealand runs regular patrols using its OPVs and air force Orion in the Southern Ocean, where fishing is regulated by the Convention on the Conservation of Antarctic Marine Living Resources.
The fishing season begins on December 1 and runs until November or until allocated fishing quotas for toothfish, krill and other species are reached.