Rob Longley of the Toronto Sun reported the team already has.
Stroman criticized the Blue Jays organization Sunday, telling reporters "it's business, man. It is what it is," when asked about his lack of long-term contract.
"Mentally, I'm ready to perform, wherever it may be," Stroman said. "I want to play here. I've been wanting to play here for a long time. I've been waiting to sign a long-term deal. I've been offered nothing. There's no one that embodies the city of Toronto more than me. And you're not going to find guys who want to come in and embody the city of Toronto because it's just not natural, and I've taken a liking to that myself, and that's been organic and natural; it's not something I had to do. That's something I wanted to do. I've always wanted to be here.
"I want to pitch in the American League East. I want to pitch against the Yankees. I want to pitch against the Red Sox. People shy away from that, people go and hide in other leagues. I'm here. I don't care who's in the box. I'll face everybody. I couldn't care less. I think that's the type of mantra and type of confidence the city of Toronto needs."
Stroman signed a one-year, $7.4 million contract in January to avoid arbitration. He has one more year of arbitration remaining before he can become a free agent in 2021.
The 27-year-old is coming off his worst professional season, posting a 4-9 record with a 5.54 ERA and 1.48 WHIP while being limited to 19 starts because of injury. He had never posted an ERA higher than 4.37 and looked like one of the most promising young pitchers in baseball in 2017.
It's possible whatever long-term deal the Jays did offer was not to Stroman's liking. Coming off such a disappointing season, the Jays could have offered him something of a lowball in hopes he'd bounce back and become a bargain.
Either way, it's clear there's a disconnect between the organization and Stroman heading into the 2019 season.