The divers have been to the location, but it was deemed unsafe due to very little visibility and swift currents.
The missing man was one of two men in an 18-foot boat which overturned while crossing the Manukau Bar.
Friends on a nearby boat managed to pull one man from the water unhurt, but the elderly man did not surface.
Police believed both men were wearing life jackets.
Senior Constable Garry Larsen of the police maritime unit said everyone in the group was upset and the people in the boat which rescued the other man were friends of the missing man and his family.
"They were all going together," he said. "The boat that capsized was following them."