The male reptile was found on September 21 in the Fitzroy River at Etna Creek, about 20 kilometres north of Rockhampton, with a bullet lodged in its head.

"Investigations into this matter are ongoing and police are appealing for anyone with further information to come forward," a Queensland Police Service spokesman said in a statement.

People for the Ethical Treatment of Animals Australia offered up to $5000 as a reward for information leading to the identification and conviction of the person or people responsible soon after the carcass was recovered. However, that is yet to be claimed.

Koorana Saltwater Crocodile Farm owner John Lever told Fairfax Media in September that the dead crocodile was "probably" the alpha-male in the area.

He said the killing would lead to other male crocodiles in the area fighting to take the title of "top croc", a battle that could be waged over several years.

However, on Sunday Mr Lever said there had yet to be any reports indicating the battle had begun. https://twitter.com/QldPolice/status/911071977456074752/photo/1?ref_src=twsrc%5Etfw&ref_url=https%3A%2F%2Fcms-authoring-production-v1.ffxblue.com.au%2Fwp%2Fwp-admin%2Fpost.php%3Fpost%3D13218%26action%3Dedit

Mr Lever, who ran a crocodile removal service across the state for 20 years, said the largest crocodile he ever caught was 4.95 metres in the late 1980s.

He estimated the dead reptile to have been at least 50, 60 or even 70 years of age.

It is believed the 5.2m reptile had been dead for a few days before a member of the public spotted it floating and notified environmental officers.

The crocodile could be one of the largest found in the wild in Australia.

The Queensland Police Service and Department of Environment and Heritage Protection were investigating the discovery. It is illegal to take a crocodile without permission, and the maximum penalty for the unlawful killing of the reptile is more than $28,000.