MLB trade rumors did a good analysis of the Blue Jays today. They're about $10-15M over the competitive balance tax threshold. Trading Turner and Kikuchi and Yimi Garcia would get them under the threshold. That's why they tried to give away Kiermaier this week. Adding Kikuchi now would put $4.7M on the Twins payroll, which should be manageable. The Jays are motivated to dump salary so he will go to the highest bidder.
I know someone else said a lefty isn't that important because other playoff teams have hit lefties but the Yankees are one of the teams where it helps to have a LH starter (20% worse vs LHP). The Yankees have a .525 OPS against Kikuchi in 63 plate appearances this year. Kikuchi has also been good vs the Royals and Ober gets destroyed by the Royals. Baseball playoffs are all about matchups.