anno aero discussed this, albeit nearly a year ago.
In a discussion about BRS the aviation analyst site pointed out that the airport has 'aggressively' promoted itself as a candidate for a MEB3 (Emirates, Etihad, Qatar) route but that runway limitations might be an obstacle.
If that is the case anno aero suggested that Turkish Airlines to Istanbul is 'the most obvious solution' for a hub link to the east.
A month or so before its BRS piece anno aero published an article about Turkish Airlines in which it reproduced a copy of a note it had acquired that showed over 30 routes the airline intended to launch in 2013. BRS was not on the list, neither was any other UK airport.
I suppose only Turksh Airlines will have some sort of idea whether BRS interests them. The airport too might have an inkling because I have no doubt the two have spoken at some time and possibly continue to do so.
The full anno aero essays referred to above, which I say again are around a year old, can be read at these links:
Bristol Airport set to hit 6m passengers again; easyJet rules the roost
The big leak: Which airports are on Turkish Airlines? route network shopping list? - anna.aero