Samsung Display, a unit of Samsung Electronics, was the sole supplier of OLED displays for Apple.
A spokeswoman at LG Display declined to comment. A representative at Apple's South Korea office was not available for comment.
Apple introduced its largest-ever iPhone and a watch that detects heart problems on Wednesday in an attempt to get customers to upgrade to more expensive devices in the face of stagnant global demand for smartphones.
The South Korean newspaper cited unidentified sources as saying that LG Display's flexible OLED panels recently passed a series of Apple's quality test.
If confirmed, the supply deal with a major smartphone maker could help LG Display gain a further foothold in the OLED display market. The South Korean company has high hopes for OLED business.
LG's mainstay, older-technology liquid crystal display business is struggling with Chinese rivals and panel price declines.
© Thomson Reuters 2018