Greene was removed from Saturday's game against the Dodgers while warming up due to a broken nail on his right middle finger, Kennedi Landry of MLB.com reports.
Greene (hand) did not pitch in Saturday's spring training game against the Dodgers, Shawn McFarland of The Dallas Morning News reports.
Greene signed a minor-league contract with the Rangers on Wednesday that includes an invitation to spring training.
The Cubs selected Greene's contract from Triple-A Iowa on Sunday, Meghan Montemurro of the Chicago Tribune reports.
The Cubs sent Greene outright to Triple-A Iowa on Saturday, Paul Sullivan of the Chicago Tribune reports.
Greene was designated for assignment Wednesday, Bruce Levine of 670TheScore.com reports.
The Cubs selected Greene's contract from Triple-A Iowa on Friday, Meghan Montemurro of the Chicago Tribune reports.
Greene will be called up to the Cubs on Friday, Jesse Rogers of ESPN.com reports.
Greene signed a minor-league contract with the Cubs on Sunday.
Greene agreed to a minor-league contract with the Yankees on Friday, Matt Kardos of MLB.com reports.