According to NVIDIA's VP of Content and Technology, Tom Tamasi, the company is happy and willing to let AMD power the new Playstation console. Citing opportunity costs and also the fact that NVIDIA were not willing to do "business at the price those guys were willing to pay". AMD's chips are also found in the recently released Nintendo Wii U.
In addition, Tom also mentioned that if NVIDIA had pursued the console business, they would have to put off other projects.
If we say, did a console, what other piece of our business would we put on hold to chase after that? In the end, you only have so many engineers and so much capability, and if you're going to go off and do chips for Sony or Microsoft, then that's probably a chip that you're not doing for some other portion of your business.
Finally, he revealed that NVIDIA's focus is on the desktop and mobile market. NVIDIA's desktop efforts had been stellar lately, but its mobile chips have been battered by Qualcomm's. However, Tom said that he hopes that will change with the refresh of Tegra 4, that will see it integrate an on-die LTE modem for the first time to boost power efficiency.