The report was of a man and a woman in the water.
A Cumbria Police spokesman said: “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 has been carried out at the river Kent to locate the man, who is in his 40s from the local area, reported to be in the water.
“Officers and colleagues from NWAS, Cumbria Fire and Rescue Service, Mountain Rescue, Bay Search and Rescue and the Coastguard have assisted in the response.
“The man has yet to be found. Inquiries are ongoing.
“Searches will resume today.”
Anyone with information is asked to contact police on 101, quoting incident number 165 of August 11.