The site - formerly Blakey's factory - is situated off Carr Crofts, Modder Place and Modder Avenue in Armley.
The iron works was famous for manufacturing shoe and boot protectors under the famous name.
Blakey’s shoe and boot protectors were invented in 1880 by Keighley-born bright spark John Blakey, Leeds Museums and Galleries said on its website.
According to the history of the factory which produced the 'segs', Blakey’s was "notorious for distributing a hideous odour throughout the district".
The factory also had its own direct rail link for receiving raw materials and distributing finished goods.
As late as 1994, Blakey’s segs could be found in 42 countries worldwide.
Goodwins of Walsall in the West Midlands bought the Blakey’s brand in 2014 and they are still produced.
In a planning application document sent on January 11, Miss Lisa McShane from Allclear Demolition Ltd said: "The site is the former Iron Works at the above address.
"It is in a very dilapidated, unsafe condition and infested with rats.
"The Council have informed us that an intruder has previously had an accident on site.
"We have fenced the area off and in our opinion the structure is unsafe and demolition would be advised."
Comments about the plans - which can be viewed here - can be submitted until February 2.
A target date of February 8 has been set to by the council.
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