Council cabinet members will consider a report recommending holding a public consultation at a meeting on Thursday.
The new school would be built on the site of Glyn Derw High School, Caerau, and replace that and Michaelston Community College, Ely.
It would welcome pupils aged 11 to 18, open in September 2018 and have indoor facilities for community use.
A new secondary school serving the west of Cardiff could be built in the next three years.