Jaye (finger) returned from the minor-league disabled list Friday.
Jaye was placed on the minor-league disabled list Monday with a right finger blister.
Jaye (arm) was activated from the 7-day disabled list at Triple-A Columbus on Sunday.
Jaye landed on the 7-day disabled list with right arm soreness.
Jaye was traded from the Twins to the Indians for cash Tuesday.
Jaye tossed 1.2 innings in relief in Thursday's 12-1 loss to the Twins, surrendering five runs on four walks and three hits while striking out a batter.
Jaye will move into the rotation and start Monday against the Indians, George Sipple of the Detroit Free Press reports.
Jaye could join the Tigers' rotation next week, likely picking up a start Monday or Tuesday against the Indians, Evan Woodbery of MLive.com reports.
Jaye (1-0) recorded his first MLB win Tuesday against the Royals. He pitched 2.1 scoreless innings, allowing a hit and two walks.
Jaye was recalled from Triple-A Toledo on Friday.