According to the Miami Herald, the Marlins have made a five-year offer worth $13 million for the hard-throwing lefty.
A standout on the Cuban World Baseball Classic squad, Chapman's fastball has been clocked as high as 102 mph.
Various reports have had more than 20 teams inquiring in Chapman. The Red Sox reportedly have offered $15.5 million for the 21-year-old.
With a large Cuban population in South Florida, Chapman would project to be a major attraction in the market.
Regardless of where Chapman signs, the lefty is expected to open the season at Double-A. But the belief among league officials is he is very close to being big league ready.
Joe Frisaro is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.