This will be an interesting placement because the characterization of Gilgamesh that is present at the start of the narrative is not the same vision at the end of it. In many ways, Gilgamesh is like Dante, himself, who must endure a journey that exists on both physical and spiritual levels in order to fully grasp his own sense of self and the evolution that is a part of his understanding of sin and redemption.
With this in mind, I think that Dante would place Gilgamesh in the circle of those who were unbaptized and thus could not follow God through no fault of their own. It is in this level that Dante has placed all of those who have achieved greatness and a sense of immortality, but have done so without the presence of a Christian God. This is critical because Dante defines redemption as one that must take place under the auspices and divine order of Christianity. Without this, Dante is strict about how redemption and a sense of liberation from the body is impossible. While Gilgamesh ends up being a wise and more understanding human being, it is inconsequential to Dante because he did so without a sense of the Christian divine helping or assisting him. It is here where I think that Dante would place Gilgamesh.