The Mets would get prized catching prospect Travis d'Arnaud. There was speculation Toronto also would receive catcher Josh Thole while sending catcher John Buck and minor league pitcher Noah Syndergaard to the Mets.
Dickey, a 38-year-old knuckleballer, was 20-6 with a 2.73 ERA last season. He is signed for $5.25 million next year, and the Mets started exploring trades after they couldn't agree to a contract adding two years.
D'Arnaud, who turns 24 in February, hit .333 at Triple-A Las Vegas with 16 homers and 52 RBIs. He tore a knee ligament in June and had season-ending surgery.
The Los Angeles Angels and Texas also had been interested in Dickey.
Out of the playoffs since winning their second straight World Series championship in 1993, the Blue Jays have been aggressive this offseason in reshaping their roster. They acquired pitchers Josh Johnson and Mark Buehrle and shortstop Jose Reyes in a trade with the Miami Marlins and signed free agent outfielder Melky Cabrera.
Dickey drew attention earlier this month when he showed up at the baseball winter meetings in Nashville - he lives in Tennessee, near the hotel where the gathering was held.
Last week, Dickey ruffled Mets management when he spoke about his contract situation during a team event at Citi Field for children displaced from their schools by Superstorm Sandy.
Dickey said it "would be disappointing" if he merely played out his option year and became a free agent.
"If that's the decision that they make, I feel like it would be unfortunate because it probably is going mean that I'm not going to be back," Dickey said at the event. "And that would be sad."