Chicago’s 40-man roster now stands at 35.
The free agency period begins Thursday.
The ninth pick in the 2009 amateur draft, Turner has a 5.97 ERA this season.
Although their three-game winning streak was snapped by the St. Louis Cardinals on Sunday night, the Chicago Cubs are starting to see progress.
Travis Wood was so dangerous at the plate Monday night that Diamondbacks manager Kirk Gibson actually changed pitchers before the Cubs starter could bat with the bases loaded in the sixth.