According to the report, the Seattle Mariners and Arizona Diamondbacks could be possible destinations for the right-hander.
The Marlins have plenty of pitching depth, and could be looking to upgrade their infield.
Turner, 22, was the Detroit Tigers first-round pick in the 2009 MLB Draft. He was traded to Miami in 2012 for second baseman Omar Infante and pitcher Anibal Sanchez.
Last season, Turner went 3-8 with a 3.74 ERA and 77 strikeouts in 20 starts. Turner also surrendered 55 walks, for a 4.12 BB/per nine innings average. He allowed one run in four innings in his third start this spring on March 13.