According to the Korea Herald, LG Display started to develop a foldable OLED display specifically for Apple. LG Display is collaborating with LG Innotek who will develop a flexible printed circuit board for the display.
It is estimated that LG display will not be able to produce such a foldable OLED until 2020. This may be a bit late for Apple as Samsung Electronics hopes to release its first foldable phone in 2018. But Apple is very keen on creating a second source for its OLEDs as it does not want to rely on Samsung Display alone.