Detectives are now studying CCTV footage of King's Lynn's waterfront and town centre to see if it can provide any clues to how and when the man entered the river.
The body was found in the tidal Great Ouse, on the West Lynn bank of the river opposite Boal Quay, on Saturday afternoon.
Firefighters were called out to help recover the remains, which had come to rest on a tidal mud flat near the riverside boardwalk.
Today police spokesman a number of lines of enquiry remained open, including reviewing missing persons records of neighbouring forces.
'CCTV enquiries are progressing to establish how the male came to be in the water,' she said. 'There has not yet been formal identification.'
Strong currents in the tidal river could have carried the body for some distance.
A post mortem is set to be carried out on the body over the next few days.
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