If £4 million plans currently being mooted by the gallery go ahead, a completely new art space could be constructed from scratch.
Alternatively two storeys could be added to the current building, which is located on Great Newport Street. This would be accompanied by a comprehensive refurbishment programme.
The gallery launched a search for architects late last week by issuing an OJEU notice.
Any new work to the current building, which is unlisted, could include an auditorium, offices and more space for exhibits.
According to the gallery, the work will be funded from several sources, including Arts Council lottery funding.