The Airini is about seven nautical miles (12km) off the coast of Karitane.
Two people rescued from the vessel about 9am today were taken back to Karitane by the Road Runner.
Maritime NZ spokesman Mark Dittmer said the boat was unable to be towed, and a warning had been broadcast to boaties to avoid the area for 24 hours.
Earlier today, the Otago Daily Times reported the partially-submerged vessel was being towed, but this had not happened, Mr Dittmer said.
Mr Dittmer said responsibility for overseeing the salvaging of the vessel had shifted to the Dunedin harbourmaster.