Citing major league sources, the website reported Sunday that the deal is contingent on the Blue Jays and the knuckleballer coming to an agreement on a contract extension. The two sides reportedly have a 72-hour negotiation window that expires at 2 p.m. ET on Tuesday.
A spokesperson for the Blue Jays declined to comment on the report.
Dickey, a 38-year-old right-hander, is signed for US$5 million next season but is seeking an extension thought to be worth $25 million over two years.
The New York Post reports that the Mets would also send catcher Josh Thole and a non-elite prospect to the Jays in exchange for catchers Travis D'Arnaud and John Buck, right-hander Noah Syndergaard and another non-elite prospect.
The 23-year-old D'Arnaud is viewed as the Jays' No. 1 prospect, while the 20-year-old Syndergaard is ranked No. 3.
Dickey, who went 20-6 with a 2.73 earned-run average for the Mets in 2012, is coming off a season in which he led the NL in strikeouts (230), ERA, innings (233 2-3), complete games (five) and shutouts (three).
Despite battling an abdominal injury, Dickey became the Mets' first 20-game winner since Frank Viola in 1990 and the first major leaguer in 24 years to throw consecutive one-hitters.
He was cut by the Mets in spring training in 2011 but worked his way to New York and earned a spot in the rotation by the end of the season.
Dickey languished in the minors for 14 years, bouncing from one team to another before finally perfecting the perplexing knuckleball that's made him a star.
He joined Dwight Gooden (1985) and three-time winner Tom Seaver as the only Mets to win the Cy Young Award.
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 off-season 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."
With files from the Associated Press.