Parnell was designated for assignment Thursday.
The Tigers opted to call up outfielder Alex Presley from Triple-A after Tyler Collins sustained a bruised knee Wednesday night, so a move to free up a roster spot was necessary, and Parnell will be the casualty. The 31-year-old had been working mostly at Triple-A this year. He allowed four earned runs on seven hits across 5.1 major league innings on the season. He'll be subject to waivers but will likely land at Triple-A Toledo.