SemiAccurate cites supposed inside sources claiming that the Sony machine is being referred to as Thebes and its Xbox rival as Kryptos.
The website also claims that the Xbox 360 successor will be powered by an AMD chip codenamed 'Oban', scheduled to go into production at the end of the year.
However, its sources also note that the quality of the processor's components was found to be "painfully low", causing delays in production.
AMD is also allegedly supplying a processor chip for the next generation PlayStation, with either Global Foundries or IBM in line to mass produce the hardware sometime after the new Xbox processors have entered development.
It was previously reported that Sony's next console would feature 4K resolution support in line with a rumored new range of Sony TVs.
Additional hardware details were leaked earlier this year, while EA's Frank Gibeau revealed that he had seen both the PS4 and new Xbox, and suggested that the consoles would introduce gaming to a further billion people.
Previous reports suggest that the next generation Xbox will include two CPUs, one for gaming and another for multimedia applications, as well as Kinect 2.0, 3D technology and the long-rumored Xbox TV.
Sony and Microsoft are yet to officially confirm any specific details of their future consoles.