A police spokeswoman told the Herald they were unable to comment further on the investigation, only that it was ongoing and no charges have been laid at this stage.
Authorities earlier made a public appeal for anyone who may have seen Gelberger that morning, including two men fishing from a dinghy off Takapuna Head.
It is thought Gelberger, a father of two young boys, began his swim route from Narrow Neck Beach about 10am that Thursday.
It is then believed he swam across Cheltenham Beach, towards North Head, with the intention of finishing at Devonport.
Police believe he was struck by a vessel, possibly a Ports of Auckland pilot boat, at some point while swimming towards North Head.
The security cameras have caused controversy, with some beachgoers who feel they are a breach of privacy.
They do not, however, breach any privacy rights, the Auckland Council says.
North Shore councillor Chris Darby said: "I understand that the cameras may be disconcerting or alarming for people in the area, especially if they are not aware that the cameras are there.
"The advice I have received is that there is nothing preventing an individual from taking a photo or video in a public place.''
Do you know anything that may help police? Contact Auckland City Police: (09) 302 6406.