“He’ll coach as long as he wants to coach,” Buford said.

Whether or not he stays on the Spurs’ bench, Popovich has committed to spending the next two summers coaching the men’s national team for U.S.A. Basketball, at the 2019 FIBA World Cup in China and the 2020 Olympics in Tokyo. An Air Force Academy graduate who was one of the final cuts from the 1972 American Olympic team, Popovich has served as a U.S.A. Basketball assistant — but this will be his first stint in charge after being named to replace Mike Krzyzewski of Duke University as the head coach in October 2015.

Among the challenges Popovich would face next season, should he elect to keep coaching the Spurs, is a turnaround of just two weeks between the end of the World Cup on Sept. 15 and the start of N.B.A. training camps.

The Spurs have recovered from their off-season trade of Kawhi Leonard, the disgruntled All-Star forward, and an 11-14 start this season — the worst record under Popovich through 25 games. A 15-6 surge since then has moved them to No. 6 in the Western Conference.

San Antonio is seeking a 22nd consecutive playoff appearance in a run that began in Popovich’s first full season as head coach. He coached the final 64 games of a 20-62 campaign in 1996-97, which earned San Antonio the No. 1 pick in the 1997 draft and the right to select Tim Duncan.