The most likely Twin to be traded should have been traded during his last good season of 2014 when he rode a .328 BABIP to hit .316 in the first half and made the AL All Star team. The Twins extended him rather than trading him that summer. This year, his value isn't quite as high as it was that All Star year, but it's not terrible. He rode a scorching hot stretch in June to get his batting average up to the respectable .292 it is right now, and brings a reputation of great intangibles to the table.
Santana got his trade value up with a quietly terrific July, only going 2-3 but pitching into the seventh inning in four of his five starts, including two complete games. Overall, his ERA dropped .72 points this month. While he isn't likely to continue pitching like that, he's established enough and has a good enough reputation for any team needing a solid, back of the rotation starter to be interested.
As you probably heard, the Twins recently shipped Nunez to San Francisco for minor league pitcher Aldalberto Mejia. It's not a bad deal for Minnesota; it was pretty obvious Nunez wasn't in the long term plans, evidenced by his abysmal .197 batting average after the All Star Break. He's actually pretty similar to Suzuki in 2014, only this time the Twins managed to deal him before he lost too much value. Mejia looks like a decent prospect, posting a 2.81 ERA this year between double and triple-A.
Veteran relievers are always wanted commodities around the deadline. Kintzler's stepped up into the closer's role with Perkins' injury and Jepsen's implosion. So far he's done better than most expected, allowing seven runs in 32 innings. Abad overcame some struggles early in the season and has pitched well of late. Both could go to any team looking for relief help, possibly the Cubs if they're still looking to upgrade after getting Chapman. The Rangers and their AL-worst 4.86 bullpen ERA could be another possible trade partner.