The Department of Fisheries is considering whether to deploy more baited hooks in waters off Esperance, where a man was mauled by a shark on Thursday.
Two great white sharks were caught by on drum lines placed in the water in the hours following the incident, which saw 23-year-old Bunbury man Sean Pollard lose a hand and part of one arm.
Mr Pollard's current condition is not known.
While he was in a stable condition on Thursday night when he was expected to undergo surgery, a spokesman for Royal Perth Hospital would not provide details of his condition on Friday morning due to the wishes of his family.
Mr Pollard had been surfing at Kelp Beds Beach at Wylie Bay in Esperance, on West Australia's south coast when the incident happened about 11am.
His girlfriend is believed to have been on the beach at the time.
Mr Pollard was rushed to the Esperance Hospital before being flown by the Royal Flying Doctor Service to Perth, where he was transferred to Royal Perth Hospital.
Video: Watch as shark attack victim Sean Pollard gets wheeled on a stretcher from an ambulance to the waiting Royal Flying Doctor Service plane at Esperance Airport.
Mr Pollard is a player with the South Bunbury Football Club which released a statement on its Facebook page yesterday in support of him and his family.
"Today a young man was attacked by a shark in Esperance. Unfortunately the young man is one of our own in Sean Pollard," it read.
"Our Thoughts are with Polly and his family from everyone at South Bunbury Football Club. We are with you all the way mate."
Wylie beach remained closed on Friday morning.
The ABC reported that Mr Pollard told authorities he was attacked by two bronze whaler sharks in what was described as a "feeding frenzy".
Both sharks that were caught on Thursday died on the capture gear and will be transported to Perth for research purposes and further examination by the department's experts.
A spokeswoman for the department said "even upon examination it may not be possible to confirm that either shark was involved in the incident this morning. It is common for sharks to disgorge stomach contents".