Blue Jays general manager Ross Atkins on Wednesday was noncommittal on Rodriguez's role for next season, Keegan Matheson of MLB.com reports.
The Blue Jays optioned Rodriguez to their Florida Complex League affiliate Sunday.
Rodriguez (1-7) took the loss against the Rays on Saturday, allowing three runs on four hits and three walks with three strikeouts over four innings.
Rodriguez allowed a run on three hits and one walk over 4.1 innings in a no-decision Sunday. He struck out two during the win over St. Louis.
Rodriguez (1-7) took the loss Sunday against the Twins no runs in three hits and two walks while striking out three over three innings.
Rodriguez (1-6) took the loss Tuesday, coughing up six runs on eight hits and a walk over five innings as the Blue Jays were downed 6-3 by the Red Sox. He struck out three.
Rodriguez came away with a no-decision in Wednesday's 11-7 loss to the Reds, surrendering five runs on six hits and two walks over 4.1 innings. He struck out six.
Rodriguez allowed four runs on four hits and two walks over five innings in a no-decision Friday against the Cubs. He struck out five.
Rodriguez did not factor into the decision in Sunday's loss to the Yankees, allowing four hits and one walk while striking out four in 4.2 scoreless innings.
Toronto recalled Rodriguez from Triple-A Buffalo on Tuesday.