Comcast SportsNet Chicago reported the Cubs had made the claim, but that the deal had not been finalized yet. Team officials would not confirm the transaction.
The Cubs could be hoping pitching coach Chris Bosio and his staff can help Turner get on track the way they did with Jason Hammel and Scott Feldman. Justin Ruggiano was Turner's teammate in Miami, and knows the right-hander well.
"He was a teammate of mine, and a great teammate, and he's a competitor out there on the mound," Ruggiano said Wednesday. "He's so young and he was a big piece in that Anibal Sanchez trade. That may have come with a little bit of pressure and may have caused him to press, I don't know.
"I'm sure he's capable of pitching at a high level," Ruggiano said. "Sometimes it takes guys a little longer to figure it out. I played against Cliff Lee when he was in Triple-A, and all of a sudden he's making $140 million twice. This game is crazy. I think Jacob has the personality that given another opportunity, he'll do OK with it."
The ninth overall pick of the Tigers in the 2009 First-Year Player Draft, Turner was pushed through the Minor Leagues quickly, and made his Major League debut in 2011 at the age of 20. He was dealt to Miami in July 2012 as part of the Sanchez-Omar Infante deal.
This season, Turner was 4-5 with a 6.03 ERA in 12 starts, and had a 5.74 ERA in relief.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.