Officers were called to Apperley Bridge on Saturday after members of the public saw a man struggling in the water.
Police and firefighters were involved in the initial search but were unable to reach the man.
A police spokesman said rescue efforts were hampered due to a deluge of water. A search of the river and its banks was being carried out on Sunday.
Efforts were also being made on Sunday to try and identify the man with police officers checking records of people who have been reported missing.
They say descriptions from people who saw him in the river suggest he is white, aged 40 and has a full beard.
The incident has been described as a "tragic event" by police who said the likelihood of finding the man "was fading."
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