Initial designs include the restoration of the building and the installation of public galleries, workspaces, a shop and an independent basement bar.
The plans have been drawn up by London-based architectural practice Carmody Groarke.
The information gathered at the consultation will inform the planning application which will be put to Sheffield City Council early next year.
The project is part-funded by the government’s Gateway to Sheffield Levelling Up Fund and the South Yorkshire Mayoral Combined Authority.
It forms part of the wider Castlegate regeneration scheme which includes the establishment of a new educational centre for young musicians and the creation of a public park in the former Sheffield Castle grounds.