These include the suggestion that the Samsung Galaxy S4 will be including a 5-inch (or 4.99-inch, to be precise) Super AMOLED display with a 1080p resolution.
With rival HTC launching its own 1080p smartphone in several countries - the HTC DNA in the US, the HTC J Butterfly in Japan - this seems highly likely to us.
According to a new Korean source, Samsung will be showing its 1080p Super AMOLED displays off at CES in January. And yes, the lack of a + sign at the end of Super AMOLED would suggest that Samsung is sticking with those PenTile displays, but let's not read too much into rumours, eh?
Moving on to those processor rumours, it's being suggested that the Samsung Galaxy S4 will run on a 2GHz quad-core variant of Samsung's own Exynos 5450 CPU.
The Exynos 5450 is built using next generation ARM Coretex-A15 architecture, which provides an estimated 40 per cent power boost over equivalent A9 chips (which is what the Samsung Galaxy S3's processor is built on).
Elsewhere, the rumours suggest that the Samsung Galaxy S4 will be getting a 13-megapixel camera.