Qatar
The two other airports rumoured to be under consideration are Gatwick and Edinburgh.
BRS is probably too close to BHX to make it a contender (and of course LHR not far away either) even if the B 787 overcomes the current runway limitations.
Three, four or five years down the line might see a different economic situation that would enable expansion to the Middle East from more UK regional airports and not just by Qatar, in which case BRS ought to be in with a shout.
I'd love to have a Middle East connection from BRS by a major airline from that region and would certainly use it but I fear I will have to wait a few years yet.