Kenyan Drake and Jarran Reed are still part of the Alabama football program despite recent run-ins with the law.
Alabama coach Nick Saban said both players are "suspended but not kicked off the team".
"When they prove that I think or we think that they're ready to come back and show a little bit more responsibility," Saban said at SEC Media Days, "and discipline for how they handle themselves, their decision making, how they represent the university, their family and themselves, then we'll allow them to come back on the team."
Drake, a junior running back, was arrested earlier this month and charged with obstructing governmental operations when he allegedly entered a taped off crime scene.
Reed, signed in January out of East Mississippi Community College, was arrested last weekend for driving under the influence.
Alabama opens the season against West Virginia in Atlanta on August 30.