A credible reputation claims that Samsung intends to launch a flexible mobile phone within a few months. Apple also looks into the game, at least judging by a number of patent applications from 2016 and 2017, which is noted by the site Patently Apple.
The patent applications describe a foldable screen that can be opened and closed as a book. The screen type mentioned is micro-led, that is, the same kind that is said to be up to date for future models of Apple Watch.
As usual with regard to patent applications, it is difficult to determine whether or not the technology described is coming into future products, but one can always hope.