Shropshire Council has been asked to consider a proposal for No. 17 Wyle Cop.
The building was previously home to the long-running sports shop, Salopian Sports.
An application submitted to the council asks permission to turn the upper floors of the building into apartments – as well as creating a fresh access on the ground level.
The new door would provide a separate entrance for the apartments, allowing the main ground floor unit to continue as a shop.
The application also requests listed building consent for the work.
A design and access statement submitted with the application shows that historically the building did have a separate entrance – dating back to the 1920s and 30s.
A decision on the plans will be taken at a later stage.
Meanwhile another application is looking for similar permission to create apartments above a Shrewsbury town centre business.
The plans are for the upper floors of 12 and 13 at Mardol Head.
The ground floor of the building is home to Cafe Nero.
The application seeks permission to change the use from commercial storage to residential, for the creation of eight apartments.
The plans also include an upper storey extension and internal remodelling.
Separate proposals could see a new home built on the site of a bungalow in Broseley that was demolished after being damaged by a fire. The proposal is for 29 Sycamore Road.
Telford & Wrekin Council has also received a number of applications, including a fresh proposal for a new housing development.
The plan, for land to the north and east of The Bridge House, on Wappenshall Road, Wappenshall, is for 15 new homes.
A former car park in Coalport could also be converted into two homes under proposals to be considered by the authority’s planning officers.
The plan would use land at the former overspill car park next to Haye House on High Street.
The proposal is for two detached homes with associated parking.