Apple currently uses OLED panels from Samsung for the iPhone X. The Korea Herald said that LG may begin shipping as many as 60 million displays for the iPhone in June, provided a deal between Apple and LG closes.
"Regarding the OLED supply deal for Apple's iPhone X, nothing has been set in detail. When anything is confirmed in detail, we will announce it, or (otherwise an announcement will be made) in a month," LG Display said in a recent filing according to The Korea Herald.
The quote suggests that discussions are ongoing but that LG is prepared to deliver displays if Apple wants them. This could help Apple manufacture iPhone X units at a faster pace. Reports suggested early supply constraints were related to the OLED screens, though Apple seems to have managed to overcome any potential supply issues.
If LG is able to build displays for this year's iPhone X, it's possible Apple will tap the company again for 2018 iPhones, which are also expected to employ OLED panels.