Hubbard, a fourth-year junior, was scheduled to meet with Crimson Tide coach Nick Saban on Wednesday to discuss his future. Saban doesn't encourage underclassmen to leave early if they don't receive a first-round grade.
Hubbard earned his degree in December. He also considered making the jump following last season.
On the year, Hubbard had 33 tackles, 5.5 tackles for loss and three sacks. In 2012, he had 41 tackles, 11 tackles for loss and seven sacks.
Earlier on Wednesday, Hubbard tweeted: "Grad school or NFL. Big decisions."