No, GE is working on a engine for the 777-300 "non-ER" or "LR". The 777-300ER will only come with GE90s producing 115K of thrust, whereas the original -300, in operation since CX started using it in `98, today is only available with Pratt and Rolls engines. So GE is known to soon be offering a suitable engine for the standard, non-ER version of the 777-300.
Read more on flightinternational.com
CO ordering any 777-300s though, is only a rumour, but GE would like to fill in a gap in their productline... and be able to offer GE90s on all current and future 777s...
Stick & Rudder