Saban benched Hurts in favor of freshman Tua Tagovailoa at halftime of the national championship game and the youngster threw three touchdown passes to rally the Tide from a 13-0 deficit to a 26-23 victory over Georgia in overtime.
"I have no idea," Saban said when asked about Hurts' future. "I expect him to be there."
Neither Hurts and Tagovailoa was declared the starter for this season after spring practice, and Saban said the matter will be resolved in fall camp.
Saban has hinted that Hurts and Tagovailoa might share playing time.
There has been speculation that Hurts would transfer if he is not the starter.
"We are hopeful (Hurts) will stay and be a graduate, regardless of his circumstances as a player," Saban said.
Hurts, who enrolled early at Alabama as a freshman, is set to graduate in December and would be able to transfer to another school without having to sit out a year to regain eligibility.
Hurts was selected SEC Offensive Player of the Year as a true freshman in 2016 and followed it up by passing for 2,081 yards, 17 touchdowns and one interception as a sophomore last season. He also rushed for 855 yards and eight touchdowns.
Alabama is 26-2 with Hurts as the starter.
Tagovailoa was Hurts' primary backup last season, completing 49 of 77 passes for 636 yards, 11 touchdowns and two interceptions.
"It's still to be determined who will play quarterback," Saban said. " ... We'll have to see who wins the team in fall camp."
The player who loses out could benefit from a new NCAA rule that allows players to compete in four games without losing the possibility of taking a redshirt and retaining a year of eligibility.