Police and ambulance crews were called to the riverbank shortly before midnight on Monday 7 April after a passerby described seeing a man in the river.
Crews including police divers spent over four hours at the scene with no success.
The search was hampered by heavy fog with low visibility.
Officers from Greater Manchester Police are continuing the search this morning, Tuesday 8 April.
Anyone with any information is asked to call police on 101.
Image: Woden Street footbridge, Ordsall – by Raymond Knapman via geograph.org