Happ, 33, pitched for the Blue Jays from 2012-14 before being traded to the Seattle Mariners last year for outfielder Michael Saunders. He was dealt midseason to the Pittsburgh Pirates and finished 2015 with an 11-8 record with a 3.61 ERA in 32 appearances (31 starts) and a career-high 151 strikeouts in a combined 172 innings. He was 7-2 with a 1.85 ETA in 11 starts to finish the regular season for the Pirates.
In 196 major league outings, Happ, who has also played for Philadelphia and Houston, has a 62-61 record with a 4.13 ERA.
The Blue Jays re-signed right-hander Marco Estrada earlier this month, but are expected to lose David Price in free agency and fellow left-hander Mark Buehrle could sign elsewhere as well. Toronto also has Marcus Stroman and R.A. Dickey in the current projected rotation with Jesse Chavez, Drew Hutchison and Aaron Sanchez the top candidates for the fifth spot barring an additional acquisition.