Lee will start at second base and bat second in Monday's game against the Rays.
The Tigers optioned Madden to Triple-A Toledo on Monday, Cody Stavenhagen of The Athletic reports.
The Tigers designated Vanasco for assignment Monday, Cody Stavenhagen of The Athletic reports.
The Tigers signed Kinley to a one-year contract, Cody Stavenhagen of The Athletic reports.
Torres is out of the lineup for Monday's game against the Rays.
Greene (hamstring) returned to Detroit on Monday and will take part in conditioning work at Comerica Park prior to the Tigers' series opener versus the Rays, Evan Woodbery of MLive.com reports.
Flaherty (forearm) threw a bullpen session Sunday in Kansas City, MLB.com reports.
Snell (2-1) earned the win Sunday, allowing two hits, three walks and a hit-by-pitch over six scoreless innings against the Pirates. He struck out six.
Clark went 1-for-3 with a walk, an RBI and a run scored in Sunday's 11-7 loss to the Royals. He also stole a base.
McGonigle went 2-for-4 with a walk, a double, a home run and three RBI in Sunday's 11-7 loss to the Royals.
