This is an excellent question, and could be a solid topic for a graduate thesis on Athanasius. The simple answer is that the authentic writings of Athanasius do not clearly support either the claim that Jesus had a soul or that he did not have a soul. Although Athanasius writes extensively of Christology, his main focus seems to be refutation of the Arian heresy by assertion of the full equality of the Son with the Father, and their consubstantiality.
In his writings, Athanasius tends to refer to Jesus simply as the Word (logos), emphasizing the way the Word and its incarnation infuse and transform the flesh, subordinating fallen and fleshly nature to the divine. In so far as the human soul devotes itself to the Word, and detaches itself from the body, the human attains a state of detachment from the world that enables reunion with the divine after death. Thus the Word, just as it enters into the flesh in the case of Christ, enters into the soul of the embodied human, sanctifying them both. This, for Athanasius, forms the basis for asceticism.
Whether Athanasius believed that Christ had a body and soul, or whether for him the Word was in a sense the soul, is a matter of ongoing scholarly debate.