Popovich was indeed an assistant with the national team, first under George Karl and then Larry Brown, with squads that flopped at the 2002 world championships in Indianapolis (finishing sixth) and the 2004 Olympics in Greece (finishing third). The subsequent decision of U.S.A. Basketball’s managing director, Jerry Colangelo, to name Krzyzewski as Brown’s replacement, instead of Popovich, spurred a frostiness between Colangelo and Popovich that took a decade to thaw.

But Colangelo had only one name in mind when Krzyzewski decided he would step down after the 2016 Summer Games in Rio. So he courted Popovich hard in 2015 and convinced the former Air Force Academy cadet to add international basketball to his Spurs duties. Popovich, for the record, agreed to take the job only if Colangelo pledged to stay on through the 2020 Olympics in Tokyo.

“This will probably be good for Pop to be able to focus on something a little bit different than Spurs business, even if it’s only for a few days,” Colangelo said. “I recall with Coach K, people would always ask him, ‘How are you going to handle two big jobs at once?’ He always said that it’s not only refreshing but, ‘I need this.’ It kept him re-energized.”

Different adjectives may apply if Leonard attends the minicamp. All eyes at the open-to-the-media workouts are bound to laser in on every coach-player interaction should Popovich and his now-former franchise player wind up in the same gym — especially with DeMar DeRozan, San Antonio’s prime acquisition in the trade with Toronto, also on the list of invitees.

But U.S.A. Basketball officials are bracing for Leonard to invoke his right to pass on the non-mandatory sessions, as LeBron James and Stephen Curry have done, as he continues his recovery from the mysterious quadriceps injury that led to the unraveling of his relationship with the Spurs. Leonard, after all, might dread the glare of the spotlight more than Popovich.

“He’s a maybe,” Colangelo said of Leonard’s attending the camp.

Popovich, mind you, is not likely to reveal much about any interactions with Leonard even if the player does show, whether in front of the audience at U.N.L.V.’s Mendenhall Center or in private.

Those who know Popovich best have said he had long been curious about what it would be like to coach beyond Duncan, even as he frequently stated publicly that he would retire with him. Yet he remains as consistent as any coach the N.B.A. has ever seen — which means you needn’t hold one breath waiting for Pop to expound on classified team business.