If we want to find an analogue in Aristotle for the notion of (transcendental) subjectivity developed by Kant and Hegel, the best place to look is in the concept of ethos, rather than in something like soul or intellect, which for Aristotle have more specialized roles. Then, going in the other direction, this Aristotelian point of view centered on ethos helps to clarify and consolidate many of the points Brandom has wanted to make about the mainly normative or ethical import of subjectivity in Kant and Hegel.
Philosophical interest in subjectivity applies especially to the transcendental kind. Traditionally, this has been situated between what was called metaphysics and something like the “rational psychology” classically criticized by Kant. With inspiration from Aristotle, Kant, Hegel, and Brandom, I’ve been proposing that the constitution of transcendental subjectivity is instead ethical at root. This seems much more helpful than the traditional version for addressing the human condition and questions of who and what we are. The values we actually live by are far more important for this than claims about the existence of some abstract entity like a personal Subject. Meanwhile, personal identity is better left outside the transcendental sphere, and located instead in our concrete emotional constitution. (See also Ethos, Hexis; Two Kinds of Character; Substance Also Subject.)