The proposed designs envision a foldable device -- remember flip phones? -- with an organic light-emitting diode screen. The company filed the patent application in July 2014 with the US Patent and Trademark Office. The news was reported earlier by AppleInsider.
Next year marks the 10th anniversary of the iPhone. There's already been speculation that at least one of the new models will get an OLED display.
Apple didn't immediately respond to a request for comment.