The British Ironwork Centre (BIC) in Shropshire wants the Knife Angel artwork - a piece exploring the devastation that weapons can bring to people's lives - to come to the city.
West Yorkshire Police has said it "very much supports" the plan and Leeds City Council said the idea was being "discussed and considered".
The 27ft structure, in the shape of an angel, took more than five years to create.
Alfie Bradley's is piece made up of more than 100,000 knives collected in a national amnesty, some of which are engraved with messages from families of victims of knife crime.
The makers wanted it to be displayed on the fourth plinth at Trafalgar Square - but a City Hall spokesman has said that "works have already been selected through to 2022 by the Fourth Plinth Commissioning Group on behalf of the Mayor of London".
It has already been hosted in Liverpool and Hull, but earlier this month the BIC, appealed to the YEP to help persuade the city to let the sculpture come to Leeds.
However, it could only come to Leeds if three authorities such as the council, a church and the police and crime commissioner come together to make sure that an intensive programme of anti-violence events take place over its 28-day stop.
Clive Knowles, BIC chairman and founder, said: "What worries us is a city having it and then it's just a PR exercise and it art and it's 'Oh yes, it's tragic' and nothing actually happens. It wasn't designed for that."
Saying that it is "probably the UK's most dangerous statue" purposely made to cause controversy, he said that hosting it comes with responsibility to educate school pupils and youth groups about the issue.
In his letter to the YEP, he said of the statue: "It is a towering memorial of hope and a beautiful homage to all the lives lost and affected by these horrific acts of violence, with many of its knives inscribed by victim's family members with messages of love and forgiveness."
He added: "The Angel ignites important debates and discussions, raises awareness, educates our youth and communities about the seriousness of knife crime, and invites a strong movement toward creating the change that is needed to end this affliction.
"To truly fulfill the Knife Angel's destiny and to have its voice heard loud and clear, it must keep moving forward and its journey must continue to every possible corner of the country that it can.
West Yorkshire had the highest rate of knife and "sharp incident crime" outside London last year, according to data from the Office for National Statistics.
Despite an initial decrease in knife crime in the region between 2010 and 2013, there has since been a rise every year with a total increase of 124 per cent from 2012-13 to 2017-18.
Detective Superintendent Chris Gibson, the West Yorkshire Police's knife crime lead, said: “We very much support the ‘Knife Angel’ coming to Leeds.
"Anything that helps to promote our key message that carrying a knife is never the answer – and that by carrying a knife you are much more likely to get attacked yourself – is positive."
He added: “Knife crime causes harm to the communities we police and misery to those directly caught up in it and we are committed to working with our partners to prevent it from happening and dealing with it when it does.
“I would always urge people with concerns about knife crime to be brave and speak out.”
A council spokesman said: "We have received a request for this particular art installation to be displayed in Leeds, which is currently being discussed and considered with partners."