Elezaj Shkelzen, 33 from Oxfordshire, was last seen on a jetski leaving Lymington for Langstone Harbour at 6pm on Tuesday, August 4.
His jetski, a white and burgundy Yamaha Waverunner, was spotted unmanned by a tanker, with a mobile phone still on board and the killcord – which stops the jetski engine should the rider be thrown into the water – removed.
A spokeswoman for Hampshire Constabulary said: ‘We and our colleagues in the coastguard have been making enquiries over the last few days but are now turning to you for your help.
‘Elezaj is described as wearing a light grey and white hoody, dark Adidas shorts, and a camouflage waterproof jacket. He may have had an orange life-jacket with him.
‘We are particularly keen to hear from anyone who saw a jet-ski being ridden in the Solent between Milford-On-Sea and Stokes Bay.’
Elezaj’s disappearance sparked a huge search and rescue operation between police, HM Coastguard, RNLI lifeboats and volunteer rescue services.
Cowes RNLI from the Isle of Wight described the rescue effort as one of the largest in the Solent ‘for some years’.
Search parties have been scouring the central and eastern Solent regions, with the majority of the hunt taking place between Southsea and Cowes.
Anyone with information, or who might have seen Elezaj since the incident, is asked to contact Hampshire Constabulary on 101, quoting the reference number 44200293979.