Moncada, 19, has worked out privately for the Yankees, Red Sox, Dodgers, Padres, Giants, Rangers, Rays, Tigers and Brewers. Other teams are expected to join the mix now that Moncada is eligible to sign.
The infielder's availability as a free agent came after Major League Baseball met with the U.S. Department of the Treasury's Office of Foreign Assets Control (OFAC) for clarification regarding new guidelines for a general license for an unblocked Cuban national, according to a memo sent to MLB clubs on Tuesday.
The contract discussions between Moncada and the interested teams have intensified in the hours since he became eligible to sign. The teenager could agree to a contract with a club sometime this month.
"I just want the opportunity to show what I can do," Moncada said. "I just want to play baseball."
Moncada established residency in Guatemala in October, and he has the documentation to meet the new general license requirements, according to his agent, David Hastings. It had been MLB's policy to require a specific license for unblocking from OFAC before it allowed a Cuban national to enter into an agreement with a team.
"My agent has done a great job, and if it wasn't for him, I would still be blocked and not able to sign," Moncada said. "I really appreciate what he and his wife have done for me. They've helped me a lot through this process, made it happen really fast. Now, we are on to the next step and closer to playing."
Moncada -- who plays second base, shortstop and third base -- starred for Cuba's top team of 15- and 16-year-olds, and he made a name for himself at the U-16 IBAF World Baseball Championships in Mexico.
Moncada made his debut for Cienfuegos at age 17 and hit .277 during parts of two seasons. He played alongside White Sox slugger Jose Abreu and Dodgers infielder Erisbel Arruebarrena. Moncada was also teammates with Abreu, Arruebarrena and other notable players like Yulieski Gourriel, Alfredo Despaigne and Jose Miguel Fernandez on Cuba's national team during the 2013 World Port Tournament in the Netherlands. Raisel Iglesias -- who signed a seven-year, $27 million deal with the Reds -- was also one of Moncada's teammates.
Moncada is on Cuba's preliminary roster for the 2017 World Baseball Classic.
His story is unique. While many Cuban players are known to leave the island in late-night escapes or defect from the national team during an international tournament, the 6-foot, 210-pound Moncada was granted his release from the Cienfuegos team last year and was later cleared by Cuba's National Baseball Commission. He was granted a visa and a passport by the Cuban government, and he left on an airplane to Central America last summer, where he trained for months before joining Hastings in the St. Petersburg, Fla., area late last year.
Moncada's first showcase for all Major League teams was Nov. 12 in Guatemala. The private showcases began a few weeks later.
"I'm really happy right now, satisfied with how things are happening, and it's all leading to me playing baseball," Moncada said. "That's the dream I've always had and I'm getting closer to making that a reality. The unblocking was a very big step."