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.

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.

“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.”