LOS ANGELES — In the not-too-distant future, the Los Angeles Dodgers could field a lineup with Cuban-born players at catcher, second base, third base and right field.

Cuban players such as Dodgers outfielder Yasiel Puig, Cincinnati Reds closer Aroldis Chapman and Chicago White Sox slugger Jose Abreu have quickly become stars in the major leagues, and now a thaw in relations between the governments of Cuba and the United States could turn the trickle of talent from the baseball-crazed Caribbean island into a steady stream.

The stakes are high. The risks are great. The rewards could tilt baseball’s balance of power.

In February, the Boston Red Sox signed Cuban infielder Yoan Moncada, then 19, for $62 million. One month later, the Dodgers spent $62.5 million on 30-year-old Cuban infielder Hector Olivera.

The money has become so great that baseball executives are debating the process by which Cuban players are acquired, currently an auction, is fair to all the teams.

There is also a question about whether Cuba truly represents the next great talent pipeline to the major leagues. There were 18 Cuban-born players on opening-day rosters this season.

The population of Cuba and the Dominican Republic is similar, about 11 million each, so the Cuban presence in the majors could rise if Major League Baseball teams are allowed to send scouts to the island and ballplayers are allowed unrestricted movement. But until then, big league clubs may struggle to assess how deep the talent pool is and what resources — equipment, instructors, facilities and the like — are required to develop it.

Although the U.S. and Cuban governments are working to restore political and economic relations, MLB enforces the current U.S. embargo by prohibiting its teams from scouting in Cuba.

As a result, major league teams generally are limited to scouting Cuban players in international tournaments or in workouts held by players who have defected or otherwise left the island.