4.7-inch iPhone 6 and the 5.5-inch iPhone 6 Plus
Apple Hiring an Engineer to Investigate Advanced Display Technologies, Including Flexible Displays
The listing, for a Senior Optical Engineer, asks for someone with experience in the design, development and technical investigation of display technologies, along with a Ph.D or M.S. in physics, optics, material science or electrical engineering.
Recent rumors have suggested Apple is looking at curved glass displays for products like the iWatch, where a flexible display could make sense -- though Apple has applied for patents relating to curved glass screens on the iPhone as well. The presence of a job listing is no indication of future products, however, and Apple's research and development labs are always investigating future products.
Corning, which makes the Gorilla Glass that is used as the front glass for the iPhone suggests flexible 'Willow Glass' displays are unlikely to appear for at least three years.
Update: The job listing seeking a Senior Optical Engineer has been removed by Apple.