Fulmer, 29, has played his entire career with the Tigers. He won the AL Rookie of the Year award in 2016 and followed it up by earning an all-star nod in 2017.
The right-handed pitcher underwent Tommy John surgery in 2019, missing the entire campaign.
This season, Fulmer has a 2.77 ERA and 38 strikeouts in 39 innings pitched for the 41-60 Tigers, who are expected to be sellers at the deadline. Fulmer threw a perfect eighth inning against the Blue Jays on Friday.
The Blue Jays are widely considered to need a bullpen boost heading into the last part of the season. Sportsnet's Ben Nicholson-Smith wrote Wednesday he'd "be surprised if their bullpen doesn't look different in a week."
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