You first port of call should be Turkish airlines, they have some cadet programming for locals which of course would be absolutely ideal for you. They are continually trying to recruit experienced pilots so it would be worth discussing with them the opportunities for employment if you were to finance your own training.
The opportunities with CTC that inabw mentioned might well not be available to non EU citizens. You will of course be able to train with them but I would not expect that you could gain employment with the likes of Easy Jet if you do not have the right to live and work in the EU.
In Cork in Southern Ireland Atlantic Flight Training offer modular courses, they are currently training some cadets for Turkish airlines so have connections with you National Flag carrier and might possibly be able to recommend you to Turkish if you trained with them and performed to a high standard. Turkish will also be placing cadets with other training schools, can you find out which they use.
As a non EU citizen please be careful of the sales pitch that flying schools will give you regarding employment opportunities, You perhaps need advice from fellow Turk's regarding airlines around the globe that will employ you as an inexperienced pilot if you can not find employment in your home Country.
Whilst Turkish continue to try and aggressively expand I do wonder how long this will last with the continued bombs in places such as Istanbul, this is bound to make travellers nervous, even those just changing aircraft, and could effect Turkish airlines future growth. The troubles will also have an effect on tourism to the coast and can not be good for the local companies offering charter flights, the holiday airline I fly for has seen a large drop in customers to destinations such as Dalaman.