The side-arming right-hander was bothered by soreness in the middle finger of his throwing hand, but he threw a bullpen session before Thursday's game against the Cleveland Indians and felt good.
Manager Ron Gardenhire said Neshek would be available only in an emergency because of the pregame throwing session, but he'll be at full strength for the weekend series at Kansas City. Neshek last pitched more than a week ago, throwing two scoreless innings April 14 against the Boston Red Sox.
Mijares is better but will stay in Minnesota to rehab during the next road trip. Condrey felt discomfort in his last bullpen session, though, and is not close to returning.