John Ward, aged 71 from Handsworth, was taking a stroll along Leveson Street on Saturday when he saw the salmon on the rocks.
He said: “I walk along the river all the time, I spotted it on the rocks and was going to dive in to get it, I’m a bit wild, but it has quite high banks.
“I’ve seen them before but couldn’t really prove it, it’s moments of glimpses.
“One of the problems is the weirs are always blocked by debris. I think if we did something about that the salmon might find it easier to get along the Don.”
The body of a 79cm salmon was also reported to the Environment Agency by a member of the public on Wednesday.
Once, the river teemed with the fish until the weirs built to power the mills blocked their path.
Pollution from factories, especially during the Industrial Revolution, then made the river too dirty for salmon to survive.
In recent years, environmental regulations has led to a dramatic improvement in water quality.
Collective work by the Don Catchment Rivers Trust, Sheffield City Council, Environment Agency, Yorkshire Water and the Canal & River Trust on projects such as building water passes has improved the habitat for salmon.
Jerome Masters, fisheries technical specialist at the Environment Agency, said: “Although this individual reached the centre of Sheffield, the final two fish passes are still needed in order to re-establish a spawning population.
“Adult salmon do not feed when they enter rivers from the sea and so have only the energy reserves stored in their body with which to propel them upstream and enable them to spawn successfully.
“Salmon only leap when they have to and prefer to swim past obstructions when they have the option. Leaping risks injury and as many attempts are often needed ‘drains the fish’s batteries’ before they reach their spawning grounds.”