Police were called at around 6:38am on the 11th August to the report of a concern for safety of a man and a woman in the water.
The woman was located out of the water and taken to the Royal Lancaster Infirmary with minor injuries and has since been discharged.
A search operation was carried out at the River Kent to locate the man, who is in his 40s from the local area.
Officers and colleagues from NWAS, Cumbria Fire and Rescue Service, Mountain Rescue, Bay Search and Rescue and the Coastguard have assisted in the response.
A Cumbria Police spokesman said: “Formal identification has not yet taken place and inquiries are ongoing.”