An e-fit of the man, who is believed to have an Irish accent, has just been released.
The kayaker was last seen at Brighton Canoes, in Newhaven, Sussex, at around 4pm on Tuesday, September 8.
His body was found on Yaverland Beach, Sandown, on the Isle of Wight on Friday, September 11.
This latest appeal by Hampshire Police follows the release of CCTV images of the man on September 22, but so far these efforts have not helped to identify him.
A police spokesman said: “Information has been shared in the force area of Hampshire and Isle of Wight, as well as in Sussex and Ireland; however we are no closer to identifying the man and need the public's help.
“We do not know where the man lived or where he was originally from.”
The man is white, believed to be in his mid-20s to mid-30s, with blue eyes and dark hair. He was described as well built and was wearing beige shorts and a blue zip-up jacket.
The kayak was a yellow and black ‘blow up’ Sevylor Conrad. The death is currently being treated as unexplained.
If you recognise the man from the description, or have any information that may help the investigation, please call 101 and ask for Newport CID.