"Every player has a right to express what he feels and what he thinks, and I think he has every right to do that with every coach or anybody in the organization who he has relationships with, which we certainly do quite often with all players at all positions," Saban said, adding that "this is probably a lot more important to people outside this organization than it is to people inside. I don't think it has any effect on our team."
Hurts, who spoke to the media on Saturday for the first time since being benched during the national championship game in January, expressed frustration with the rumors about his future and how there were "people making decisions for me."
The junior, who is 26-2 in his career as a starter, was also critical of the coaching staff's handling of the situation.
Saban said he had talked to a lot of the team leaders, and the players are "focused on what they need to do."
He added that the situation with Hurts isn't something that has impacted the Tide "one way or the other."
"The rhetoric will not have anything to do with who's the quarterback," Saban said. "That will obviously be decided on the field by how people execute, how they do their job. The same parameters that we've talked about before in terms of who wins the team. And winning the team goes along with execution, leadership, players having confidence and belief. And that's not going to change."
Players told reporters on Tuesday that they met as a group to talk about Hurts' comments. Veteran offensive lineman Ross Pierschbacher said the meeting brought "closure" to the situation, while senior running back Damien Harris said it wasn't "a big deal in-house."
Hurts, who threw one interception last season, is locked in a quarterback battle with sophomore Tua Tagovailoa. Tagovailoa played in mostly mop-up duty during the regular season until coming off the bench at halftime of the national championship game and threw three touchdowns, including the game winner in overtime against Georgia.
Hurts said he was "shocked" when Saban told reporters at SEC media days that he had "no idea" whether Hurts would be on the roster opening day, even though Hurts said that he had made it clear beforehand that he was intent on staying and graduating in December.
"That's always been the elephant in the room," Hurts said Saturday. "For me, no one came up to me the whole spring, coaches included, no one asked me how I felt. No one asked me what was on my mind. No one asked me how I felt about the things that were going on. Nobody asked me what my future held. That's that. So now it's like when we try to handle the situation now, for me, it's kind of late, it's too late, the narrative has already been created."
Alabama, which checks in at No. 1 in the USA Today Preseason Coaches Poll, opens the season on Sept. 1 against Louisville.
In addition to deciding on a starter, the Crimson Tide must replace all four starters in the secondary and incorporate new offensive and defensive coordinators.