The 21-year-old left-hander is headed to either the Los Angeles Angels or the Jays within the next "three of four days" according to the SunSentinel.com of Fort Lauderdale.
Chapman defected when the Cuban national team was in Holland in July. The report estimates a $21-million US signing bonus already is on the table for him. The Marlins had made a $13-million offer.
During the World Baseball Classic, the 6-foot-4, 180-pound lefty's fastball was clocked at 100 m.p.h. against Japan.
Jays general manager Alex Anthopoulos is trying to negotiate the deal while on his Hawaiian honeymoon.