With roughly 200 kilograms subtracted (how they will manage to take this much weight out is anyone's guess) the F-Type Coupe would get down to the ~3200 pound range. That would put it much closer to something like a 911 GT3.
This is what F-Type program director Russ Varney had to say, "We have three or four things we are looking at for the next developments of the F-Type and a lightweight, harder version is a long way up that list. If you could get a couple of hundred kilos out of it, that would be a special car. We won’t get any weight savings of significance by looking at any one thing, so it has to be holistic across every part and that’s a lot of engineering."
If this car would use a tweaked version of the 550 horsepower supercharged V8 or a new motor is unknown. When this car would come if it does is unknown as well. We will have to see what happens but a much lighter hardcore version has a high degree of enthusiast appeal. Let's hope Jaguar does it.