Doctors will reevaluate Jones when he returns from Christmas break on Dec. 27.
Jones rode a stationary bicycle with a cast on his left foot during Tuesday's practice and is "day to day," according to Saban. Ryan Kelly took snaps with the first-team offense in Jones' absence.
"Everything (Jones) is doing is precautionary," Saban said.
"I'll be playing in the game," Jones said emphatically. "I'll be fine."
Jones, who won the Rimington Award for the nation's top center, has helped Alabama to a balanced offensive attack. The Crimson Tide rank 20th in rushing yards with 224.6 yards per game and average more than 38 points per contest.
The redshirt senior already has two national championship rings and could play for a third when No. 2 Alabama faces No. 1 Notre Dame in Miami on Jan. 7.
Jones wasn't the only Alabama player nursing injuries during the Tide's first day of bowl practice on Tuesday. Starting nose guard Jesse Williams wore a black no-contact jersey and former starting wide receiver Kenny Bell, who broke his leg against Western Carolina, did the same. Saban said Bell has been cleared to play but his availability against Notre Dame is undetermined.
"I can't make a call as to whether he'll play or not," Saban said.