The sperm whale was found at Old Hunstanton in north Norfolk on Christmas Eve. By Boxing Day, its lower jaw was gone.
The BBC has published the picture of the man Norfolk Police wish to speak to, having already spoken with a juvenile and his family about the offer for sale of the jaw and teeth on Facebook.
The jaw held 11 teeth. Another 15 had been removed and were being offered for sale as individual pieces.
The removal of the jaw was in contravention of a ban on harvesting by the International Whaling Commission (IWC).
Sale of the ivory would contravene a ban on trade by the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES).
Only certain societies are allowed to harvest and trade set amounts of sperm whale ivory, usually where there is a tradition of scrimshaw.
Britain is a signatory to the IWC and CITES regulations.
Contraventions under British law have occurred under The Conservation of Habitat and Species Regulations 2010 and the Wildlife and Countryside Act 1981.
Further, the remains should not have been disturbed without the permission of the local council and of the Maritime and Coastguard Agency.
The man being sought was photographed on the beach at Hunstanton at about midday on Christmas Eve.
Respondees should contact PC Rob Willis at Hunstanton Police Station on 0845 456 4567, or Crimestoppers anonymously on 0800 555111.
From its state, it was clear that the whale died some time before it was washed ashore.
Its corpse was removed in early January, after tissue samples had been taken for analysis by the Zoological Society of London.
The Society maintains a UK database on cetacean strandings. From analyses of creatures that have died, researchers can determine the difficulties which they have faced.
These include natural and infectious diseases, starvation, entrapment, injury through attack by other creatures or collision with vessels, and contamination from toxins either in the sea itself or in the food chain.
Related links
British Divers Marine Life Rescue
First UK sighting of whale species