Joakim Soria is off the board. So are Darren O'Day (basically), Ryan Madsen, Mark Lowe, and a number of other reliever targets. The Winter Meetings have a way of accelerating everyone's timeline, and this year is no exception.
The top left-handed reliever left on the market could be Tony Sipp. And if Jerry Crasnick is correct, his desired contract perimeters have been announced.
Teams that have inquired on LHP Tony Sipp say he's looking for a Zach Duke-Boone Logan type contract. Three years, $5-6M per.— Jerry Crasnick (@jcrasnick) December 7, 2015
Sipp, entering his age-32 season, has posted a 2.66 ERA, 2.93 FIP, 0.96 WHIP, and 10.7 K/9 over his last two seasons - 105 innings in 109 appearances. He's been good versus both right and left-handed hitters, holding righties to .613 OPS this past summer and lefties to a .599 OPS. He does average less than an inning per appearance, but for those numbers you could hardly do better.
There's not hard traction between the Twins and Sipp at this moment. But here's hoping he's near the top of the Twins' hit list.