"I don't know the answer," he said, per Marc Stein of the New York Times.
"He'll coach as long as he wants to coach," team president R.C. Buford added.
According to Stein, Popovich and Buford have "periodically discussed the club's various options after this season."
Popovich will serve as the head coach of men's USA Basketball for the next two summers, however.
The 69-year-old has already secured his legacy as one of the greatest NBA head coaches in basketball history. He's gone 1,223-561 in his 23-year career, winning five titles in six trips to the NBA Finals. Under his leadership, the Spurs have made the postseason 21 straight years and, with a 26-20 record this year, appear on the way to making it 22 years in a row.
Popovich doesn't have a core in place the likes of Tim Duncan, Manu Ginobili and Tony Parker, though DeMar DeRozan (21.7 PPG, 6.1 RPG) and LaMarcus Aldridge (20.5 PPG, 8.5 RPG) have played well this season.
However, the loss of Dejounte Murray for the season in October hurt whatever slim title chances the Spurs had. One of the questions Popovich will have to consider is whether he wants to remain with the Spurs if they're unable to build a roster capable of competing with an elite team like the Golden State Warriors.
The Spurs are unlikely to have cap space this summer, barring some personnel moves, so adding another superstar could be difficult. Of course, Popovich may still love coaching, title contender or not. But it's hard to imagine the state of the Spurs won't factor into his decision.