The Rangers, Yankees, Cubs and White Sox have expressed the most interest in signing the left-hander, according to Concepcion's agent, Jaime Torres. The Marlins, Phillies, Giants, Blue Jays, Red Sox and Royals have also shown interest.
Concepcion has one offer on the table, and is expected to sign a Major League contract during the next two weeks, the agent said.
"Everything is great. I really don't know how to describe it," Concepcion, 18, said by phone from the Dominican Republic. "All the training and exercise I have done is paying off. I've worked so hard to get here. I'm so happy. It's like a dream come true."
Concepcion, who was named Rookie of the Year in the Cuban Serie Nacional in 2010-11, after posting a 10-3 record and a 3.36 ERA in 21 games with Industriales de la Habana, defected from Cuba last June during the World Port Tournament in the Netherlands. He later established residency in Mexico, and was declared a free agent last week.
He has been working out in the Dominican Republic and starred in a showcase for Major League scouts on the island last Thursday.