User blog comment:Xilinoc/Ch. 568. Hear. Fear. Here 2/@comment-1604252-20140212213631/@comment-26420452-20140213162757

Special War Powers are only five and they're decided based on Yhwach's judgement. Take Genryūsai, undeniably the strongest Shinigami we know up to now, and the only reason he was not classified as one was because Yhwach just wanted not to give any importance to him, despite, well, the first invasion's purpose was just killing him.

The only one who has a slight possibility (0,00000000...1%) to be one is Byakuya. He's a master of Shunpō, Kidō, Zanjutsu and has one of the most versatile and deadly Bankais out there, however he doesn't any quality that makes him to be above the captain class, like Yamamoto, Aizen, Ichigo or what supposedly Ichigo has become. Well, until now, he may have become absurdly powerful after his stay in the Royal Palace.