The Knife Angel, which is made from knives used in stabbings, is touring the country but will not be coming to the city.
Coun Paul Wood, cabinet member for community safety, made the decision after talking with groups and individuals, who were completely divided on it. But he says he is happy to reverse the decision if there is overwhelming support for it.
Danny O’Brien, who set up the national campaign group Anti-Knife UK, had some input into the creation of the Knife Angel by the British Ironwork Centre.
Mr O’Brien, who set up the campaign group 11 years ago, said: “Every one of the police forces, including South Yorkshire Police, have given knives towards this sculpture.
“Sheffield is the city of steel and most knives are made from steel. It sounds horrendous but when you see it, it’s a marvel and it gets people talking. I have been to Liverpool and Coventry to see it as you need to explain to people what it’s really about.
“It’s not glorifying knife crime and could be used by schools to show that it’s not cool to carry a knife.”
Mr O’Brien isaid he was hoping to change the council’s mind.
He added: “There’s plenty of time for it still to come to Sheffield. Most cities are putting it outside the Cathedral so it could go outside Sheffield Cathedral and it’s only here for a month. It would bring in tourists from outside Sheffield too.
“It would show Sheffield is doing something. Families have been affected by knife crime so this is somewhere they can remember their loved ones or lay flowers. You could build on it by getting the football clubs to support anti-knife crime campaigns.”
Coun Wood said he would like to hear more people’s opinions on whether the Knife Angel should come.