Search activities continued over the weekend but a spokeswoman for NSW Surf Life Saving told news.com.au it had no assets taking part in the search for remains today.
On Sunday six drones, eight jet skies and a Westpac Rescue Helicopter surveilled the coastal waters of Sydney's eastern suburbs to keep a lookout for shark activity and to continue the search for remains.
A NSW Police spokeswoman told news.com.au the latest update from the Marine Area Command on Sunday suggested police officers were continuing to search the area, as part of their investigation into the shark attack. However, no further update was available.
News.com.au has also contacted the Department of Primary Industries and Westpac Rescue Helicopter for details of any further search activities.
Last week, half a wetsuit and some human remains were found in the aftermath of the attack.
Mr Nellist is thought to have died during the shark encounter off the rocks, with nearby rock fishers observing the attack.
A great-white shark is suspected of killing the diving instructor but the animal has yet to be found. Authorities are also awaiting the results of DNA testing.
The family of Nellist are now thought to be making arrangements to fly from England to Australia to mourn the "proud Cornishman" who emigrated to Australia and was living with his fiancee Jessie.
"Simon was funny, compassionate and always had time for people. He had a rare gift of instantly being able to connect with others, gaining their trust and respect," his family told the BBC.
"Simon had a great passion for nature and the sea, as well as being a very talented photographer."