A seating area and gardens could be created around Pinfold Steps, off Shambles Street, but there will be no disabled access.
Plans have been submitted by Barnsley Council for a 'high quality open space' for people to 'gather and sit in the enjoyment of a well designed and landscaped area'.
A walkway will also be created between Shambles Street and Westgate including contemporary seating, lighting and planting. But a report said the steep access to the site presented 'an impossible design constraint to making the new open space accessible to wheelchair users'.
The report added: "Access ramps if provided through the site would take up all the open space land and would be a costly engineering scheme requiring a sum of money, it is estimated, at least equal to the funding available for the open space improvement."
The council secured Growth Point funding from the Leeds City Region for the project which must be spent by June 30. More on this story, including the heritage of the site, in Friday's Chronicle.