This rumor is reported exclusive by a Korean paper, claiming inside info from Samsung officials, and we already heard a similar claim by another Korean publication, but no size was mentioned then. What we can grasp from Google's translation, is that Samsung has been dedicating resources into the Full HD AMOLED, instead of mobile LCD arena, since it is the OLED-based displays that are its differentiating factor before the competition.
Given that the Droid DNA just appeared, the Sony Yuga and Odin are coming with 1080 screens next year, LG shouldn't be far behind as it has a Full HD LCD panel developed, and Sharp is now selling an Aquos SH903W in Russia with a 5" 1920x1080 display of its own making, it is only logical that Samsung is prepared to wow with something different. The AMOLED panel is claimed to be very thin, with low power consumption, as well as high contrast and refresh rate, which are staples for OLED-based screens, but we'll save judgement for when we eventually see it at CES.
The official said the display is with 441ppi pixel density, which is pretty close to the perfect human vision. A combination of the current FMM production method, suitable for mass production, and the more advanced LITI technology, which is cheaper, but can't be scaled sufficiently, is supposedly being used to arrive at the 5-incher with 1920x1080 resolution.
It reportedly depends on the mass production scaling whether we are to see this thing in the Galaxy S IV in Q2 next year, but Samsung has a few months to work out the kinks, and it already proved it can do an excellent non-PenTile HD Super AMOLED in the Note II with a new production method, so we are keeping our hopes high. The source also says that the Samsung Electronics chief demanded that a Full HD AMOLED be used in the S IV, instead of an LCD, as that's the company's unique proposition, so the engineers seem greenlit to trash another football field of display glass and figure it out.
Moreover, we were tipped back in September that Samsung flaunted a 5.8" ClorOLED screen with 358ppi, allegedly for the Note III, so next year might indeed shape up to be the year of Full HD mobile screens, be they LCD or AMOLED, for flagship phones across the board.