Adelaide police are treating the discovery of a man's body in the River Torrens, near the University of Adelaide in the CBD, as suspicious.

A member of the public found the body and called police just after 2:00pm.

Police divers recovered the remains just after 3:00pm, 50 metres west of the Adelaide University footbridge.

Officers said the man was believed to be aged between 40 and 60, and he was not carrying identification.

It is not yet known how he died and police would not comment on whether there were any obvious injuries.

Officers said it was too early to say how long the man's body had been in the water.

Police have started a search of the river and the surrounding riverbank between the Adelaide Zoo and King William Street.

An area east of Kintore Avenue has been cordoned off.

Anyone with information has been urged contact Crime Stoppers.