The BBC has contacted officials to confirm the reports.
The Department of Primary Industries and Regional Development (DPIRD) said it was assisting police and local authorities with the incident.
It has also urged residents to report any shark sightings, local media report.
It comes less than a month after a father-of-two died after a separate shark attack in Western Australia.
Steven Mattaboni, 38, was attacked by a 4m (13ft) shark at Horseshoe Reef, north-west of the popular Rottnest Island near Perth.
Shark attacks around Australia are more common than in many other parts of the world, though they are often not fatal.
Popular swimming and surfing spots tend to have measures to protect against attacks.