LG Electronics is set to unveil its next flagship phone, the G5, on February 21st. The company published a short teaser, saying that the new phone will have an "always on" display that shows the time and notifications:
Such an always on screens is highly suggestive of an OLED display - as an LCD will still require a lot of energy to display even a small amount of pixels because it uses a backlight. An OLED will only consume power proportional to the number of lit pixels.
However, it is quite unlikely that LGE will use an OLED display - because to do so they will have to buy these OLEDs from Samsung Display, as it's not likely that LG Display will be able to supply enough OLED panels.
LG Display does produce OLED displays, but in a very limited capacity, in a Gen-4.5 fab (14,000 monthly substrates) that produces flexible (plastic-based) OLEDs. LG currently mostly makes small flexible OLEDs for wearables (such as Apple's Watch and LG's own Watch Urbane 2). LG makes a single handset flexible OLED, the curved 5.5" FHD panel adopted in the company's own G Flex 2 - but this was never really a mass produced device, and I can't see LG supplying enough OLEDs from this fab to a flagship mobile phone.
LGD announced plans to build a Gen-6 (1500x1850 mm) flexible OLED fab in a $900 million investment. The new E5 line will be located at LGD's Gumi Plant and will have a capacity of 7,500 monthly substrates - or 1.5 million 5.5" panels. But the new fab is scheduled to begin mass production in the first half of 2017... so it won't be ready for the G5.
There are some reports that LG Display does aim to enter the mobile phone market with its flexible OLEDs, and actually aims to do so in 2016 - but they will probably start with lower-volume phones (reportedly LGD is in talks with Chinese phone makers Vivo and Oppo).