The incident, which happened on Thursday 7 September at around 14:40, was reported to Jersey Coastguard by multiple witnesses.
The Acting Harbour Master went to Belcroute Bay to speak to the paddleboarder on shore, while the pilot boat crew made contact with the jet ski at sea.
Anyone who has information should email Jersey Coastguard on jerseycoastguard@ports.je or call 01534 447705.
Jersey Coastguard also issued a reminder that all users of watercraft, which includes jet skis, must abide by the Harbour inshore safety regulations which can be found online here.