AIBA president Ching-Kuo Wu visited Cuba this week to discuss the cream of the country's fighters joining the professional-style World Series of Boxing and soon to be launched AIBA Pro Boxing.
"They are very serious about it," Wu told Reuters by telephone on Friday. "We have cleared the way for them and they are very happy and are very seriously considering joining subject to final approval by the Cuban authorities."
Cuba could field a team in the WSB when the fourth season starts later this year, Wu said.
Cuba is the second most successful boxing nation at the Olympics after the United States with a total of 34 gold medals.
However, the likes of late heavyweight Teofilo Stevenson, who won three golds, were never allowed to fight as professionals because of the country's restrictive rules introduced by the country's former leader Fidel Castro in 1962.
While some boxers, like Joel Casamayor, defected to the US and turned professional, Wu believes the WSB and APB can now provide the perfect bridge between the amateur ranks and the professional game for Cuban fighters.
Previously, boxers who fought as professionals were barred from competing at the Olympics.
"I think they are very comfortable to join because it gives the boxers the ability to return to the Olympic Games," Wu said. "The WSB is a very important step forward for Cuba."
The WSB, an international team event, features boxers competing for franchises such as the Mexico Guerreros, Argentina Condors, British Lionhearts and Ukraine Otamans.
Unlike in the amateur ranks there are no headguards or vests and boxers receive payment.
Seven boxers from WSB teams won medals at last year's London Olympics including Ireland's lightweight John Joe Nevin, Italian heavyweight Clemente Russo and Ukraine's heavyweight gold medal winner Oleksandr Usyk.
Wu believes a team representing Cuba would help the growth of the competition.
"Cuba is one of the strongest boxing countries in the world with a great Olympic and world championships record," he said.
"During the visit we informed them of how it (the AIBA) has developed in the last six years. To have them join the WSB and the APB would be a major step for us.
"The whole thing to have the Cubans to join the programmes would be an historical moment.
"Boxing is the number one sport in Cuba so this visit has been most important because it was a complete exchange of views and it answered many questions. We have a mutual understanding."
Later this year the AIBA will launch the APB, a fully-professional 10-weight individual competition which allows boxers to retain their Olympic eligibility.
More than 100 boxers will qualify for the Rio Olympics through the WSB and APB, compared to the five fighters who arrived in London by winning WSB weight divisions, Wu said.