The N.B.A.’s concerns relate to player health, broadening the sport’s appeal, finances and perceived arrogance of the International Olympic Committee. At this point, any change seems more likely to occur for the 2020 Summer Games, yet to be awarded, than for the 2016 Olympics in Rio de Janeiro.

“It might be time to step back and, if nothing else, to satisfy the owners so they can begin studying it,” David Stern, the N.B.A. commissioner, said in a telephone interview from New York. “Frankly, the more I whistled a little tune, the more I said, ‘Maybe you stumbled onto something.’ I’m not sure this changes anything, but it’s time to take a look.”

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Team owners, having invested hundreds of millions of dollars, worry that their star players will become fatigued and injured. The 12 United States players here are perhaps less of a concern than the 26 global N.B.A. players, who often face enormous nationalistic pressures to represent their countries at the Olympics and in continental tournaments, even when hurt.

It is widely believed that Yao Ming’s career was shortened by foot problems developed from a grueling schedule of playing for the Houston Rockets and the Chinese national team.

In 2008, the prime minister of Lithuania phoned Stern, asking him to help persuade Zydrunas Ilgauskas of the Cleveland Cavaliers to play at the Beijing Games. The country was considering allocating public money to provide insurance for the fragile Ilgauskas, whose pre-existing injuries left him less than fully covered for the Olympics. Stern declined to pressure Ilgauskas, and he did not play in Beijing.

Increasingly, Stern has grown intrigued by soccer’s 32-team World Cup, held every four years, extending for an entire month, unencumbered by simultaneous competition from other sports. By contrast, Olympic basketball is limited to 12 teams over 17 days and must share the limelight with two dozen other sports. The N.B.A. and its players are also severely restricted in leveraging marketing opportunities with sponsors not associated with the Games.

FIBA, basketball’s international governing body, does conduct a world championship every four years. Although that tournament is more popular than the Olympics in some countries, the Summer Games dwarf the world championships as a basketball showcase in the United States. Recently, the name of the tournament was changed to the World Cup in an attempt to broaden its appeal.

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Mark Cuban, the owner of the Dallas Mavericks, wants the N.B.A. to stage its own World Cup, without FIBA’s involvement. That way, money would be more equitably shared with various national basketball federations and N.B.A. players, Cuban wrote in an e-mail. He has also grown impatient with the I.O.C., which he views as supercilious, greedy and exploitative of the league’s players as Olympic programming for NBC.

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“They are risking their futures so that the Olympics organization can maximize sponsorship and TV deals,” Cuban wrote. “There is no good reason for the N.B.A. to risk our athletes so they can profit.”

Stern is more diplomatic. He prefers not to simply decree that the N.B.A. will no longer release players older than 23 for the Olympics. He has spent 20 years engendering good will with FIBA and does not want to be viewed as a heavy-handed, ugly American.

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FIBA is also in a sensitive position. A number of countries fear that the United States, given its population and depth, would have a greater advantage in an under-23 Olympic tournament than it does now with N.B.A. players.

FIBA’s secretary general, Patrick Baumann of Switzerland, is also an I.O.C. delegate and is said to be torn. On one hand, he wants to make the basketball World Cup more relevant. On the other hand, Baumann knows that an under-23 Olympic basketball tournament would be severely devalued, like the soccer competition. (Sepp Blatter, the president of soccer’s governing body, FIFA, is also an I.O.C. member, but he operates from a position of much greater strength, given soccer’s unmatched popularity.)

Some Olympic officials would welcome reduced N.B.A. involvement in the Summer Games. Athletes in individual sports, effectively seen only once every four years, would have a greater chance to gain attention. But other officials see risks for the league in an under-23 format: accusations of hubris and lack of patriotism, a decline in global visibility of the sport, a threat to international development.

“Maybe not in America, but in the rest of the world, the Olympics might be the only time people will see basketball at that level,” said Michael Payne, a former marketing director for the I.O.C. “If you suddenly think you’re so strong and no longer need that, well, how many other brands, how many other entertainment properties, think they’ve arrived and then, poof?”

Expanding the basketball World Cup might also put greater physical demands on N.B.A. players. Soccer is locked in a continual struggle between club and country. Would the N.B.A. be willing to do what FIFA does, set aside dates during the season when clubs must release players for national team games, often requiring brutal travel?

If the N.B.A. does maintain its current Olympic involvement, it may be for this reason: The players say they love it. They attract a global audience. They rub shoulders with top athletes from other sports. They have fun in a festival atmosphere while playing for a gold medal.

According to USA Basketball, the national governing body, the performance of Olympic players often increases in subsequent N.B.A. seasons. Kobe Bryant dismissed the under-23 idea as stupid. Carmelo Anthony said players should be allowed to decide on their own, regardless of age, whether to represent their country.

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“David Stern’s views are based on him protecting his players,” said Pops Mensah-Bonsu, a British forward who formerly played for the Mavericks and the New Orleans Hornets. “But it’s the Olympics. If you put age limits, you’ll take away from what it really means.”