The animals are understood to have been flown in from the United States and remain in quarantine.
Details regarding the tests are expected from Biosecurity New Zealand by mid afternoon.
There is a risk of a "false positive" or that the animals have had the disease but are no longer infected or contagious.
It is believed further testing is under way.
Horses coming to New Zealand from the US must be vaccinated against equine influenza, between 42 and 120 days before export, using "an approved inactivated vaccine either twice not less than 21 days apart, or once as a booster to a previous primary course of vaccination," according to the Biosecurity NZ import standard.
Also, once a horse has been in quarantine in the US for at least five days, a nasal swab must be taken and tested negative for EI using a PCR or antigen ELISA. The standard was issued on October 1, 2007, and Biosecurity NZ said the latter requirement was "an interim emergency measure and will be reviewed in the future".
Australia is only now recovering from its equine influenza outbreak, which began last August. The disease is widely thought to have escaped quarantine near Sydney, and subsequent eradication efforts cost an estimated $A100 million. The equine industry suffered losses estimated to be around $A500 million.
Senior counsel at the inquiry into the outbreak, Tony Meagher, argued last week in his final submissions that even rudimentary quarantine measures at the quarantine station in question would have prevented the virus's escape into the wider horse community.