Perkins hasn't stepped on the diamond since April 10, pitching in just two games this season.
Kevin Jepsen took over as closer after Perkins was shelved but was ineffective.
In June, manager Paul Molitor gave Fernando Abad and Brandon Kintzler the closer duties. Minnesota also claimed Neil Ramirez off waivers on June 12 and he has logged plenty of strikeouts in his career.
The Twins have recorded just 8 saves this season, which ranks dead last in baseball.