Neither Byzantium nor Turkey have any territorial aspirations worth persuing.
With reguards to Turkey they'd sure like to reclaim the Greek portion of Anatolia, Cyprus and Byzantium but realistically thats not going to happen short of war, which is not in the best interests of the Republic of Turkey. Therefore we have resigned ourselves to our current borders, nothing more, nothing less.
The only borders Turkey would be willing to discuss would be the Island of Kuzi Lemani which is currently Atlantean, Byzantean and Turkish controled, quite a muddled state of affairs. Its quite possible that with the right incentives either Byzantium, Greece or Atlantis could possess the Island entirely.