Alex Khan has announced his intentions to build the homes on land at Keeton’s Hill.
The proposals include one studio, four one-bedroom apartments, eight two-bedroom homes and a three bedroom apartment.
A design and access statement submitted with the application said the site was currently used as a car park and external storage area.
It said: “The proposed building is predominantly three storeys in height, stepping up to four storeys with a set back on the top floor.
“The fourth storey adheres to the ‘25 degree rule’ with exception to the lift shaft and its impact is therefore not considered to be harmful to the neighbouring properties.”
The plans do not include any parking.