Part of Ysgol Glan Clwyd in Saint Asaph will be demolished in November, with new classrooms, assembly, music, drama and dining areas created.
Work is aimed at meeting growing demand for Welsh-medium education.
Denbighshire council's cabinet will be asked to approve awarding a contract for the work to Willmott Dixon.
A £15.9m Denbighshire school construction project is set to get under way after a firm was chosen to carry out the work.