While there are rumors that Apple could be working on a foldable iPhone, the company has continually looked at the possibility of rollable displays for a future device β including an iPhone with a rollable screen.
According to a newly-revealed patent application (via AppleInsider), Apple is considering just that: βAn electronic device may have a rollable display. The display may be moved between an unrolled state in which the display is planar and a rolled state in which a rollable portion of the display is rolled up for storage.β