Ortiz, 40, made one appearance this season, throwing 3 1/3 innings in Toronto's 7-0 loss to the White Sox on April 17. He allowed two runs on five hits in the outing.
The Blue Jays have 10 days to trade Ortiz or offer him his outright release. He could also be claimed off waivers by another club.
Laffey, 28, has appeared in four games for the Mets this season, posting a 7.20 ERA. In 22 games, 16 starts, with the Blue Jays in 2012, Laffey went 4-6 with a 4.56 ERA.