The Twins were hoping to compete this year after a surprising improvement in 2015, but an 0-9 start put a serious hitch in that plan. They've gone 11-23 since, and while they should regress enough to avoid their current 120 loss pace, they would need to play .500 ball the rest of the way just to avoid a 90 loss season. The playoffs are essentially a pipe dream at this point, and so the potential for a sell-off is already there.
Because the team is on pace for a losing season, there's not a lot of incentive to bring up any of their top prospects from the minors. Byron Buxton and Max Kepler may be better served getting consistent at bats at AAA and saving on service time in order to keep both players under team control longer. Add in the amount of years and money committed to the top of the starting rotation, and they're also likely to leave Jose Berrios at AAA to ensure that he works out his issues with walks.
The hard part with looking for possible trade candidates on the Twins is that this team isn't exactly stocked with veterans or impending free agents. Some of the players that the Twins would likely love to unload like Kurt Suzuki, Brian Dozier, and Ricky Nolasco are simply not playing well enough to interest anyone in a trade. You've also got a lot of players that aren't likely to be viewed as upgrades to contenders, such as Eduardo Escobar, or players who are simply owed too much money like Phil Hughes. With all that said, there are still two players who, if traded, I can see leading to increases in the fantasy value of other members of the team.
Trevor Plouffe (3B)
Plouffe was a trade candidate during the offseason once the Twins had signed Byung-Ho Park, and could look to move Plouffe again before the deadline. He's currently hitting .245/.270/.387 with 3 home runs through 28 games, and spent some time on the disabled list at the end of April.
In terms of potential teams he could go to, it's most likely to be a team that either suffers an injury to their everyday 3B, or one that is looking for a platoon power hitter who can play either corner infield spot. Either way, the return is not likely to be particularly interesting despite him being under team control for another season still.
With a Plouffe trade, you're looking at a series of dominoes which hopefully starts with Miguel Sano moving back to 3B, and any number of combinations of Max Kepler, Oswaldo Arcia, or Eddie Rosario getting more regular playing time. Arcia remains the most interesting in terms of power potential, but it's clear that the team views him as a platoon player primarily. I would bet on Kepler being the one who gains the most overall fantasy value, capable of providing decent numbers in four categories.
Kevin Jepsen (RP)
Jepsen was expected to be the 8th inning reliever for the Twins this year, but the injury to Glen Perkins moved him back an inning. The potential increase in value that might have come from him notching another 10-15 saves in the first half has all but dissipated with his poor start.
Jepsen is a free agent after the season, and as such would likely be one of the first players dealt in a sell-off. Finding saves can be difficult at midseason, and while there is a likely opportunity here, it's not exactly clear which direction the Twins would go. Michael Tonkin has been pitching the 8th inning lately, and would make the most logical sense based on how he's pitching.
However, it's not clear that the Twins are operating in a logical manner at all with their bullpen or their roster in general. They've moved Alex Meyer up and down, used him in the bullpen and the rotation and now have him back at AAA, waiting for another opportunity. Trevor May would have been an interesting candidate until his recent struggles, and it's not clear that the Twins have any interest in bringing any of the number of relief prospects in the upper minors up anytime soon either.
If I had to speculate right now, I'd take a shot on Tonkin, but remember that the Twins have only had 12 save opportunities to begin with, converted just 3, and don't particularly appear likely to have a massive increase in save opportunities going forward.