Korean website ETNews is reporting that ZTE will be announcing its own "4G mobile chip" as soon as next month:
China's C114 reported that ZTE would disclose the semiconductor for 4G devices it developed next month at `PT/Expo Comm China 2013.' According to ZTE, this chip is compatible with 4G data communication and processing standards and advanced enough to lead to the development of 4G. ZTE did not disclose the details of this chip, but C114 said that ZTE worked hard to develop processors in the wake of Apple and Samsung Electronics. The industry forecast that this chip is an integrated application processor with communication functions.
That's not a whole lot of info to go on, but it seems pretty clear that the chip will have an LTE modem integrated into it. However, the more interesting parts, the actual processor and the GPU, are unknown, and we can only guess what it could be.
The article says that ZTE has been looking to Samsung and Apple for what kind of chips it can build. I doubt ZTE built its own custom CPU core, and they probably intend to follow Samsung's lead, and use a stock ARM core, such as Cortex A7, Cortex A15, both of them, or the upcoming Cortex A12 CPU, but that's a year away, and unless they just plan on announcing it now, and not release it with their new products this year, then that's pretty unlikely.
Huawei is also getting ready to finish its own 2nd generation processor, the K3V3, which will be an "8-core" chip, much like Samsung's Exynos 5 Octa, made of a quad core Cortex A7 CPU and a quad core Cortex A15 one. ZTE has always been a main rival of Huawei in many markets, and I could see why they didn't want to be left behind on this. Making their own chip means they could save a few bucks on their smartphones, instead of having to buy them from Mediatek or Qualcomm.
The nice thing about the ARM chip ecosystem, is that it's an actual ecosystem of companies building their own ARM SoC's, so the competition is a lot higher than it would ever be in the x86 chip market, and I don't think we'll ever have to worry too much about lack of competition in the mobile chip space, regardless of whether Intel's or Imagination's MIPS chips get any traction.