Louise Walsh was asked to design a piece as a tribute to the factory girls of the city.
But the unfinished sculpture remains in an engineering yard after planning permission was not granted for any of the potential sites.
Ms Walsh identified King Street roundabout as her chosen site, but Roads Service had safety concerns over the location for such a large object.
A DSD spokesperson said efforts were made to find a suitable alternative.
"A number of options were explored, including sites at or adjacent to the location of former shirt factories, but the artist felt that a site behind the Guildhall was the only option which was prominent and prestigious enough to meet the purpose of paying tribute to the factory workers," they said.
The department said it intends to meet with project promoters, the City Council and the artist to discuss whether the sculpture can be reworked to be located behind the Guildhall, depending on planning permission, or to locate it elsewhere.
The spokesperson also said they would examine other options to commemorate the role of the factory girls through another piece of artwork separately commissioned.
The artist claims a redesign of the project will push the original budget of £90,000 to over £150,000 and she fears those costs won't be met.
"I have been put aside a load of other work to try and resolve it," Ms Walsh said.
"I just don't think there is a place to go with it for me now unless I get approached to get funding to get this moving."
Those who worked in the city's factories feel there should be something to mark Derry's industrial past.
"We think that the sculpture should be put up as a lasting memorial to the factory workers, that are alive and who've gone- our grannies, our mothers, whoever worked at the factory at the time," former factory girl Isabel Doherty said.
Ms Walsh also added: "These women worked so hard, and really have not been celebrated in the way they should and I think there should be some kind of civic space that's dedicated to them in the city."
Derry City Council said in a statement: "Derry City Council, with lead partners, Department for Social Development (DSD) and Central Procurement Directive (CPD) in the Factory Girls project, see the project as an important and fitting tribute to the significant roles played by the female factory workers in the city.
"The Council continues to demonstrate a civic commitment to public art and fully acknowledges the significance of celebrating art and culture as it hosts the first ever UK City of Culture in 2013."