Samsung is going to make several different versions of the Galaxy S4, including the Galaxy S4 Mini, Galaxy S4 Active, and Galaxy S4 Zoom. As you can imagine the Galaxy S4 Mini is a smaller version of the regular S4, but it seems it won't have a much weaker chip, as usual. Instead, it will be using another one of Samsung's big.Little chips, but this time instead of being a 2 cluster quad-core chip, it will be a 2 cluster dual core chip, combining a dual core Cortex A7 and a dual core Cortex A15 CPU.
This shows that Samsung is fully committed to the big.Little architecture and also to its owns Exynos chips, and it's very possible we won't be seeing a Qualcomm chip version, even in US, if Samsung manages to finish the integration with LTE modems for its own chips. This seems to have been the main reason why Samsung went mainly with Qualcomm's S600 chip for the regular Galaxy S4, but have already said that they will start using more Exynos 5 Octa chips once they get the LTE integrated version.
Other specs for the upcoming Galaxy S4 Mini include 4.3" Super AMOLED qHD display (should be 720p by now), 2 GB of RAM (3G territories will only get 1 GB of RAM), 32 GB of internal storage, 8 MP camera, and a 2,100 mAh battery. The Cortex A15 CPU will be clocked at 1.6 Ghz, while the Cortex A7 one should be clocked at the same 1.2 Ghz.
So it looks just like the Exynos 5 Octa, but with half the cores, most likely to cut costs, since mobile chips are paid for by the core. The leak states the device will be running Android 4.0, but I expect it to ship with the exact same version of Android and Touchwiz that is on the Galaxy S4. Android 4.0 would make zero sense at this point in time. And I doubt Samsung would release something with a "Galaxy S4" in front that has an older version of Android.
There's no rumored release date, but it should be officially announced/launched in the next few weeks, otherwise the difference in time between the regular S4 and the S4 Mini might be too large.