WASHINGTON — At a dinner in one of Fidel Castro’s palaces in 1999, Castro and several of Major League Baseball’s senior executives discussed one of the few bonds between Cuba and the United States: baseball.

The executives, including baseball’s commissioner, Bud Selig, were there for an exhibition game between the Baltimore Orioles and the Cuban national team, as part of an effort by President Clinton to thaw relations.

As the dinner stretched into the early hours of the morning, Castro regaled Selig with tales of Cuban baseball and fantasized about what would happen if the United States and Cuba normalized diplomatic and economic ties. Castro told one of the executives, Sandy Alderson, who had overseen preparations for the trip, that he was open to the idea of major league teams having academies in Cuba. They would be similar to the ones in the Dominican Republic, where teenage players honed their skills in hopes of making it to the majors.

Fifteen years after that dinner, the vision of an active relationship between Cuba and Major League Baseball became a little more real Wednesday after President Obama’s announcement that he planned to restore full diplomatic relations with the island nation.